A modern day world much like our own, where it is common to be born with 'Quirks', powers, or super powers. As a result superheroes are regulated forces, superstars, and trained from highschool age in specialized hero schools.
Type: Blossom
As a world where superheroes are the norm, most player chaarcters and their powers are likely to be seen as 'commonplace'. It stands to reason that a character could head to the MHA world and join a super group, gain fame and status, and become a public figure, or find a new livelihood
Superheroes or supervillains could wander out into the tree and explore other worlds, providing aid or performing acts of evil as they seek to spread territory, or people from worlds where powers are persecuted could head to the MHA world to hide and blend into the population seamlessly.
The world government will ultimately treat new arrivals like people with Quirks and request registration, though ultimately there will be those who fall through the cracks, players from outside worlds can handwaive the registration process. Ultimately the government will have to brace for an influx of new people, but the populace will likely not be surprised by people from other worlds displaying super abilities, however there will likely be reaches for trade, cultural, and technological exchange where possible.
UA Hero Academy and the teachers will begin encouraging potential new heroes to intern under heroes and larger than life figures from off world in order to exchange culture and learn how the grander universe of the Tree beyond compares to the laws and rules of Japan, and in order to encourage the students and heroes to interact with characters from beyond the My Hero Academia world.