You are, of course, very much aware of this: indeed, this is seen clearly where you write “more or less”. You clearly agree that the state and federal governments have every right to interfere, and set up limits on what decisions the local government can make about its schools.
Moreover, you agree that the state should only be getting involved in “deeply extreme cases”. Well, guess what: there is no objective way to specify what is “deeply extreme”. In fact, DeSantis and his supporters will tell you that the books being curated away are, in fact, “deeply extreme”. You are of course free to disagree, but that’s the point: your objection is not at all about the right of the state government to do the thing it is doing (you believe that the government should totally be able to do exactly what DeSantis has done), only about the contents of the decision, which is to say, whose ox is being gored. Why don’t we discuss that, instead of engaging in silly discussions about the extent and limits of governance, which in today’s America have been, for better or worse, definitively settled with practically zero chances of being changed any time soon?
The state's job is to set up and maintain a structure by which localities etc. can more-or-less self govern their methodology of education and handle things like content, and e.g. fire your hypothetical school person who's glorifying Nazism. And the actual state should only be getting involved in deeply extreme cases, if at all.