There is a connection though, Persona 1 and Persona 2 Eternal Punishment indeed happened and is continued by Persona 3 (Persona 2 Innocent Sin). One connection is the Forced Persona User Experiments on Persona 3 in which the Nanjo Group (Kei Nanjo`s group from Persona 1 and 2) is helping the Kirijo group on that. And…

That’s why he goes to the “gym”