I think it all has to do with impact. The point of the first amendment is so that the government cannot create policy to chill speech it doesn't like. That's why we all appreciate it.

A small branch library making autonomous choices about what books to store behind its walls with backing of the local community doesn't stand to chill speech across the state or nation, so the first amendment protection to free speech isn't really implicated. If some podunk town doesn't want to put books about trans kids on the shelves, that's not going to chill speech about trans people across the state or nation.

But when the governor sets policy that no libraries shall have books about trans people, then that's going to chill speech and the first amendment is implicated. Therefore it's unconstitutional, despite flowing from the same derived power source. That's my view anyway, I'm not a lawyer.