Not all defined tags for registry are present in data pack after switching between worlds

When a tag is defined via a data pack that is loaded in one world, that tag stays defined on the client side and is not removed even if the player logs out of a world and joins another world.

01:12:15.191
Not all defined tags for registry ResourceKey[minecraft:root / minecraft:item] are present in data pack: minecraft:bookshelf_books, minecraft:hanging_signs
01:12:15.191
Not all defined tags for registry ResourceKey[minecraft:root / minecraft:block] are present in data pack: minecraft:all_hanging_signs, minecraft:ceiling_hanging_signs, minecraft:wall_hanging_signs

Also affects 1.20 snapshot game built-in data packs.

Steps to Reproduce:

1. Create a new world with the attached data pack.
2. Look at some grass blocks, dirt, sand, or waxed copper.
3. In the F3 menu, notice that there is a line #test:tags_persist_across_worlds.
4. Save and quit to title.
5. Create or join another world with cheats enabled but without any data packs beside the vanilla data pack.
6. Look at some grass blocks, dirt, sand, or waxed copper.
7. In the F3 menu, notice that there is still a line #test:tags_persist_across_worlds, which should not be there given that the data pack providing the tag is not present in the current world.
8. Check the client logs. One or more lines of the following form would have been printed.
   Not all defined tags for registry ResourceKey[minecraft:root / minecraft:block] are present in data pack: [...], test:tags_persist_across_worlds