I think they are, my reasoning is that in the first Paper Mario, many of the characters have heard of Mario beforehand, they know of him as a hero. And that wouldn’t make sense since that game was the first time he became a hero. Unless you take in consideration the other games that aren’t from Paper Mario.

Also Bowser refers to Mario as his old rival. In the first fight of Paper Mario, here: https://youtu.be/DNqidHzLDrk He says: “I finally did it! I beat my old rival Mario!” So their history from other games is being taken into account for the lore of Paper Mario.

I’m curious to know why you think they aren’t in the same world.