JWA fixes the parameters so implementations interoperate: MGF1 uses the same hash as the signature, and the salt length equals the hash length (32 bytes for PS256, 48 for PS384, 64 for PS512). Signatures differ on every call because of the random salt; verification still takes one public-key operation.
FAPI security profiles require PS256 or ES256 and exclude RS256, and TLS 1.3 likewise uses PSS for RSA handshake signatures. Because keys are shared with RS256, an issuer can migrate by publishing alg: PS256 keys (or the same key with a new kid) and switching verifiers to accept PS256.