Thanks for testing against prerelease Pythons! I would add the classifier at the time you get the tests green, but continue to make releases as per your usual schedule.
I wouldn’t think reasonable folks would interpret the package as being abandoned. I think it’s kind of silly to think something is abandoned and switch without a) checking the actual project (which in your case would have active commits demonstrating testing on new Python), b) having a direct unmet need (needing something merged/released). And enough people don’t bother doing minor version classifiers or let them get stale that there’s plenty of company.
That said, I guess if your last release was years ago and your last classifier was like 3.6, I’d probably assume that your software is either done or abandoned. And it’s fine for software to be done. And it’s also fine to make non-functional releases at a cadence of your choice as a way to communicate liveness and ongoing testing to users.