As of 12th March 2018, the Potterverse has a new name for the whole Harry Potter franchise - Wizarding World.
This term covers the whole range of Harry Potter media, not just the original seven books.
Do we want to create a new tag [wizarding-world] as the new catch-all tag for questions set in the Harry Potter world?
As far as I can tell, the arguments in favour of such a change would be:
Granting greater distinction between questions about the Harry Potter books and questions about the Fantastic Beasts films, The Cursed Child and other parts of the franchise. Given that this is a constantly expanding franchise, we're going to have an increasing quantity of questions tagged with [harry-potter] which actually aren't about Harry Potter the character at all. Since the [harry-potter] tag is already very big it would arguably be helpful to distinguish clearly between questions based on the seven books and those based on other parts of the franchise.
There is a precedent for tagging this way elsewhere on the site - for instance, separating [lord-of-the-rings] questions from [the-hobbit] questions whilst still having the catchall [tolkiens-legendariam] tag for them all.
'Wizarding World' is the new official term by which the franchise-creators wish the works in question to be referred. 'Harry Potter' is not an official term in the same way. Having the proper name in tag form makes the site look good. Lacking it doesn't.
The arguments against:
Retagging all 5,174 (and growing) questions would take a Herculean group effort akin to the big edit event and muck up the front page for a bit.
'Harry Potter' is well known as a term of reference whereas 'Wizarding World' isn't (yet).
There are doubtless other points I haven't thought of. I don't have a strong opinion either way but thought that I should open it up to community discussion.