In most attacks, the data on that site is compromised and changing your password afterwards just prevents further exploitation by others.
What some password manager do is monitor for shared passwords (i.e. using the same password on Site A and Site B). This prevents attackers from cracking the password hash offline and trying the username/email and password in a bunch of different sites.
It’s not completely hands off (and I don’t know that I’d want it to be… there are a few passwords I don’t want it changing without my knowledge), but it’s something.
I think the full use case you describe is better suited for a passkey manager, since passkeys are marching generated already.