This is not an event/activity that is related to passing legislation, nor does it fit under the category of any of their usual business.
Keep in mind that the filibuster is a Senate rule, and is not enshrined in law in any way. Each session of government, the Senate sets up the rules under which they will operate (and to a certain degree, some Senate Majority leaders have decided they can just ignore their own rules, since they are the ones who decide whether rules have been violated or not).
The first thing that prevents Senators from filibustering is that they are not active participants in the trial. They are the jury, so to speak. In a normal trial proceeding, there is no time allotted for the jury to speak, argue or present during the trial. So that would be a limiting factor.
What also prevents a filibuster in a Senate impeachment trial is the fact that, when they create the rules under which that specific trial will operate, they don't include the filibuster as part of it. If they decided they wanted it to be there, and, say, grant unlimited time for Senators to speak when if they are allowed to comment on why they are voting as they are, they could.
While some parameters are set by the Constitution - Chief Justice presides, 2/3 vote required, there is no standing set of detailed procedural rules for an impeachment trial, itself. The rules of each individual trial have been and are set by that Senate, once the impeachment is delivered by the House.
The Senate approved ground rules for President Donald Trump’s impeachment trial that include unexpected concessions addressing
some of the Democrats’ concerns about the process. But Republicans did
not budge on Democrats’ resolution amendments that would commit to
witness testimony and subpoenas for documents (as opposed to waiting
until after opening arguments). The resolution passed 53-47 along
party lines early Wednesday morning after more than 12 hours of tense
debate between the House managers and Trump’s legal team.
Following weeks of back and forth between Democrats and Republicans,
Senate Majority Leader Mitch McConnell on Tuesday abruptly backed away
from two key pieces of his proposed resolution released Monday night.
One change redistributes the total number of hours that House managers
and Trump’s defense team will have for opening arguments — instead of
two days, they will each present for the same amount of time over
three days. Another change allows evidence gathered in the House
impeachment inquiry to be included in the record.
PBS: The impeachment trial rules are set. Here’s what happens next
As you can see from that article about the Senate passing the resolutions that set the rules for Donald Trump's trial, it was very much up to the Senate to determine the process and procedure for what would, and would not be allowed, and how much time different parties would have to present.