The events of Star Trek IV: The Voyage Home establish that humpback whales are sentient beings with their own language, and that this language is at least in theory learnable by non-whales (e.g. the probe apparently speaks it despite not being a whale). We also see Spock mind-melding with a whale, and he reports that he was successful in communicating.
Considering the principles of the Federation, this would seem to indicate that humpback whales would be recognized as intelligent beings with rights from 2286 onward. Is there any indication that this is the case or that this is specifically not the case? Are whales in the 24th century considered to be Federation citizens with the same rights as humans and Vulcans? Are they non-citizens of the Federation but recognized as sentient beings with civil rights (e.g. can't be owned ("not the hell your whales"), allowed freedom of movement, etc.)? Do any whales serve in Starfleet?
To be clear, I expect that the budgets for The Next Generation and even beyond did not really provide for much room to include regular or even guest-star whale characters, but do we hear anything about what happens after Kirk and company bring whales back from extinction in 2286 and demonstrate to the world that they are intelligent? Do they receive immediate full Federation citizenship? Is there a gradual process where they are integrated into Federation society over a period of years or decades, receiving more and more rights and responsibilities as time passes?
Also to be clear, I'm not asking about how whales would physically navigate human-designed starships or cities or whether there are whale-designed starships that are built to cater to cetacean needs over those of humanoids. Those are plot and setting details rather than answers to the fundamental question of whether whales receive the same basic civil rights possessed by humans.
The Memory Alpha page on humpback whales is surprisingly sparse and doesn't indicate what happens to the descendants of George and Gracie.
As for how practical communication would work, there would clearly be some people (both whales and humanoids) interested in learning each other's language(s). Gillian Taylor, struggling to restart her career in the 23rd century as humanity's only remaining whale expert, would likely be first in line to learn Whale. By Picard's time, I would expect there to be a fair number of humans who are fluent Whale speakers as well as a few English-speaking whales. Maybe whales discover that they have trouble with pronouncing English so they type it on keyboards or sound it out in Morse code, I don't know. Those would be interesting story points! There would probably also be room to update the Universal Translator as necessary (if updates are necessary at all) to include accommodations for whale grammar, phonology, etc. to allow whales and non-whales to speak to each other about whatever they feel the need to talk about.
Implied evidence is acceptable. If there are whales that hold Starfleet rank that is other than purely honorary, that would answer the question. Likewise, evidence that whales have the right to vote in Earth and/or Federation elections, hold public office, hold professional licensure, sit (float?) on juries, or otherwise exercise any of the civil rights normally restricted to natural persons under the law counts.
If it's established somewhere that George and Gracie are unsuccessful at reproducing and their species goes extinct again shortly thereafter, I would count that as an answer.
