You unlock most suits by reaching a certain overall Spider-Man level in the game, but you’ll still have to pay for the ones you want to fully unlock with in-game currency like Tech Parts or the much rarer Hero Tokens. Most suits have these styles, though some (typically those based on movies) do not. There are also suit styles, which offer different colorways of suits for a fee (of in-game currency).
Unlike in Spider-Man 2’s predecessor - 2018’s Spider-Man - suits in Spider-Man 2 are purely cosmetic.
How to unlock all suits in Spider-Man 2 on PS5