There's clearly some kind of difference because I've been mass-adding "isekai" as a user-defined tag on dozens of games, but it is not one of the selectable boxes when I search through the games in my own library I know I have added this user-defined tag through.

At what point do user-defined tags graduate into 'store tags' that will show up as search options on our launchers?

I think maybe steam should keep track of any user tags we have manually added to games in our library and make them a checkable box too.