The most substantial of the efforts in the linked material, in the sense that at one point they erupted into mass protests and armed conflicts, are those in the Caucasus region, especially Chechnya. The civil war with Russian troops there was long, bloody, and ruthless on both sides.
It makes sense that independence movements would be most intense there. This is an area that is predominantly Muslim in a secular/Orthodox Christian country, is an area that is highly linguistically and culturally distinct from the rest of Russia, and is a place that had received partial autonomy prior to the break up of the Soviet Union and saw that autonomy diminished rather than expanded after that happened.
This conflict was largely put to bed, however, with unrest quelled and the military aspect of the insurgency largely quelled, when Vladimir Putin reached a personal agreement with the leaders of the insurgency. See, e.g., stories in the Washington Post and at the BBC. The deal made was basically for these leaders to shut down their insurgency, in exchange for being granted the privilege of serving as Putin's unofficial private army and enforcers in a manner that didn't have quite the legitimacy of a formal branch of the military, but was tolerated and allowed to operate with impunity.
Some of these units were deployed in the Ukraine conflict this year, which proves that the deal remains in force and is being honored by both sides.
So, there really aren't any potential breakaway regions in Russia for which discontent over the current war in Ukraine would tip into meaningful successful action or a renewed and effective insurgency.
On balance, popular unrest directed at replacing leaders in the national government of Russia or getting the national government to change course policy-wise, in a manner similar to the events that led to the breakup of the Soviet Union and what followed in the early days after this happened, would appear at this time to be a more likely possibility.
UPDATE on March 25, 2022
Upon reflection, there is a possibility that is outside the letter of the question but captures its spirit that i didn't address the first time around.
This is the question of some sort of popular action or insurgency against the existing regime not in Russia, where by most accounts, Vladimir Putin's regime reinforced by well honed totalitarian means of suppressing dissent and to quote Chomsky, "manufacturing consent" makes this very unlikely, but in Belarus.
Technically, Belarus is legally independent of Russia already. The "union of Russia and Belarus", a supranational confederation, was established in a 1996–99 series of treaties that called for monetary union, equal rights, single citizenship, and a common foreign and defense policy, but for reasons that seem somewhat obscure and muddled to outsiders, this has never been implemented.
Instead, for quite a few years, Belarus has acted like a tributary state of Russia that while independent in name, actually slavishly follows the lead of Russia on all matters upon which Russia has a meaningful opinion as an unequal partner. And the leaders of Belarus, all of whom for all practical purposes, report to Alexander Lukashenko, have performed their duties in a style that mimics Putin's leadership approach.
In particular, Belarus has, at the governmental level and officially, at least, fully cooperated with Russia and been a critical co-conspirator of Russia in facilitating Russia's invasion of Ukraine, and Belarus likewise, has suffered almost all of the sanctions and boycotts that the international community, public and private has imposed upon Russia. Yet, so far, Belarus has mostly just made its territory and some of its hand me down second rate military equipment available to Russian troops to carry out their invasion of Ukraine.
But, while Belarus seems homogeneous enough that there is no regions within it that would be likely to consider succession, the analysis that leads informed observers to conclude that Putin's hold on Russia is completely secure does not apply with equal force to Belarus.
The most obvious and glaring example of the potential for resistance by (at least some of) the people of Belarus is the fact that on Tuesday of this week, an organized group in Belarus sabotaged rail lines from Belarus into Ukraine, which were critical for providing logistics support to Russian troops advancing in Kyiv, in order to impede the Russian invasion of Ukraine.
This incident embarrassed the leaders of Belarus so much in the eyes of their patron, Vladimir Putin, that Belarus is now talking very seriously about adding its own troops and best military equipment to that of Russia as a fully participating partisan ally of Russia in the invasion of Ukraine for which it is being punished anyway in international circles.
But, the political calculus is not the same.
Belarus gained independence without a fight in 1990 with the other former Soviet Republics. President Alexander Lukashenko was elected President under a newly adopted more Western style constitution in 1994 and was re-elected in 2001, 2006, 2010, 2015 and 2020. A series of trade disputes erupted between Russia and Belarus starting in 2004 and Lukashenko's efforts to return Belarus to a more Soviet style centralized economy gave rise to a severe economic crisis in 2011, hyperinflation, and a horrific public transit bombing in which 15 people were killed and 204 were injured (whose immediate perpetrators were swiftly caught and executed the next year) swirling with unanswered questions about their motives ranking from terrorism to a false flag attack designed to prop up Lukashenko's government. As explained by Wikipedia at the link at the beginning of this paragraph:
Mass protests erupted across the country following the disputed 2020
Belarusian presidential election, in which Lukashenko sought a sixth
term in office.[ Neighbouring countries Poland and Lithuania do not
recognize Lukashenko as the legitimate president of Belarus and the
Lithuanian government has allotted a residence for main opposition
candidate Sviatlana Tsikhanouskaya and other members of the Belarusian
opposition in Vilnius. Neither is Lukashenko recognized as the
legitimate president of Belarus by the European Union, Canada, the
United Kingdom nor United States. The European Union, Canada, the
United Kingdom and the United States have all imposed sanctions
against Belarus because of the rigged election and political
oppression during the ongoing protests in the country.
The official result, in which Lukashenko won 80% of the vote in 2020, reflects corruption in the election administration process and not widespread support for man described as "Europe's last dictator."
Taken together, this is the stuff of a real regime changing protest movement willing to take some direct action and already having internationally recognized outside leaders and an existing organizational structure. Despite being only secondarily culpable so far in the Ukraine invasion, Belarus was arguably facing worse sanctions as a result of the disputed 2020 election than Russia did a result of its 2014 annexation of Crimea and support for insurgent forces in Donbas in Eastern Ukraine.
Unlike restive regions within Russia, Belarus has a direct border with Western aligned Lithuania, Latvia and Poland that Russia cannot easily block. Until June 28, 2021, when Belarus severed its ties over international criticism of and sanctions based upon its flawed 2020 election, Belarus had significant economic ties with the E.U. that a new regime could restore.
The likelihood of Russia using its nuclear weapons against Belarus for breaking away from it politically following a coup or insurgency or other regime change in Belarus seems much less likely than Russian use of nuclear weapons in response to direct NATO intervention with its own member's military forces in Russia's war with Ukraine.
While it isn't terribly large, 4.8% of people in Belarus are part of Ukrainian or Polish minorities disinclined to continue of status quo of supporting Russia.
Unlike Russia, Belarus has neither nuclear weapons nor operational control over natural gas shipments to the rest of Europe upon which Europe is heavily reliant.
While the benefits that Russia hopes to achieve from its Ukraine invasion at great cost are somewhat cryptic, the benefit of the invasion to Belarus other than satisfying its Russian liege, are basically nil. Prior to the immediate build up to the invasion, Ukraine had no real quarrel with Belarus, and presumably could easily make peace with Belarus if it parted ways with Russia.
Not least of all, while Lukashenko has tried to be a totalitarian leader of Belarus in the image of Putin, he simply hasn't been as competent in his capacity to exert total control over his country, to completely control the media, and to suppress dissent as Putin has been. This is so even though Belarus had already been kicked out of the European Human Rights authority known as the Council of Europe in 1997, while Russia was just ejected after it invaded Ukraine in 2022, a quarter of a century later.
While it may or may not be a majority of eligible voters in Belarus, there is a widespread and invigorated mass resistance movement already in place in Belarus which has support from far more than the 20% of voters who official voted against Lukashenko in the 2020 election, and that opposition would probably surge if it appeared that there was a viable path to a successful regime change for the opposition. Some people in Belarus are keeping their heads down and not getting involved simply because they fear retaliation from an authoritarian regime with a history of human rights abuses and not because they actually have any attachment to Lukashenko's government.
So, if there is a grass roots uprising of the kind the question considers anywhere involved with Russia that could change the political balance of the situation, it is in Belarus, and not in Russia proper, which Putin has firmly locked down.
This said, I am not saying that such an uprising is even necessarily more likely than not. It is very hard to upset an entrenched authoritarian regime even with international support, particularly when Russia might back up Lukashenko's effort to hold onto power in much the way that it did in January of this year when it sent in a small military force to help the leader of Kazakstan put down in mass protest and uprising there.
But, this is by far the most likely place for something along the lines of what the question is suggesting to happen, and while it may not be more likely than not, it is also not a remotely unlikely possibility, given the great uncertainties and constantly evolving situation in Europe caused by the invasion of Ukraine.
Also, an uprising and insurgency in Belarus wouldn't need to be immediately successful to divert troops that would otherwise be sent by Belarus to Ukraine to be on hand to maintain order in the event of an insurgency at home, and to interrupt the extent to which Russia can stage operations in Ukraine from Belarus aimed at the Ukrainian capital of Kyiv seamlessly and without hiccups as it managed to do until Tuesday of this week when the rail line to Ukraine from Belarus was sabotaged.
And, with the war in Ukraine going badly for Russia compared to almost everyone's expectations, Russia needs to devote all of its available military resources to that fight and might not be able to spare troops to prop up Lukashenko in Belarus the way that it did in Kazakstan earlier this year before the invasion. Realistically, Russia would be compelled to divert at least some troops from the operations in Ukraine to do so, since Belarus is a crucial base of operations for Russia in the Ukraine war, and that would weaken Russian forces in Ukraine.
So, the bottom line is that a serious uprising against Lukashenko in Belarus, even if it failed in a manner reminiscent of the failed uprising against absolute monarchies in Europe in the year 1848 that only actually achieved their primary goals a quarter century later, a serious attempted by failed uprising in Belarus, which is far more likely than a fully successful one, could still have a significant impact on the ongoing Russian invasion of Ukraine, to Ukraine's benefit and Russia's detriment.
