How should such questions that were once acceptable but are now off-topic be handled?
Flag, or vote to close, as off topic.
This is a point that both Monica Cellio and myself made in answers to Notices for our traditions: Anatomically correct (and Santa). Several people also made similar arguments in the comments to that question. And of course, I'm plenty sure that similar arguments have been made elsewhere as well; this is just the one I happened to be able to find quickly, and it's reasonably recent (December 2017).
The simple fact here is that standards change for a multitude of reasons. Questions that were at one point deemed to be on topic are determined by the community to fall outside of the site's scope.
Questions that fall outside of the site's scope should be put on hold. If those questions can't be fixed, or aren't fixed, then they transition to closed status.
There's no need to actively go looking for such questions, but if you come across them, including by them being pushed into the review queues, then it's perfectly allowable to vote to close if they don't fit the current standards.
If the question was acceptable and considered on topic at the time it was posted, and has received answers, then there's probably little room for fixing it much later without invalidating answers, so the normal on hold, improve, reopen process doesn't readily apply. However, you can still leave a comment along the lines of "I'm voting to close this question because it is no longer within the site's scope because <reason>".
For questions that have seen a lot of answers and voting, there exists the possibility to apply a historical lock on the question, which among other things prevents further voting and informs visitors that while the question was at one point acceptable, it no longer is, so should not be used as a justification for posting similar questions. Especially once a question has been closed, you can flag it for moderator attention and suggest a historical lock, and we'll look into it. Historical locks don't apply everywhere, but they are one way to inform visitors of the fact that site standards have changed since the question was active.
The same reasoning holds for both the main site and for Worldbuilding Meta.