So then how come the Metaverse works completely differently in every game?
The thing is that the Metaverse is only in Persona 5. I know Mementos in Smash Bros has Persona 3 and 4 versions, but that's just pure fanservice.
In Persona 1, demons just start randomly invading the real world and another dimension.
In Persona 2, rumors around town start affecting the reality of the world, like Hitler and the Waffen SS suddenly invading Japan.
Persona 3, there's now another hour between midnight and 1 AM that spawns this huge ass tower from your school.
In Persona 4, you go inside TVs.
Continuity really does not exist beyond the cameos except in the Arena games, strangely enough.