How long are cloud backups stored by Bitwarden?

This is documented in the Help Center:

Bitwarden has configured a strict 7-day retention policy for PITR [point-in-time restore] and a policy of no long-term retention.

Also, Bitwarden does not back up the actual database, but instead maintains a log of individual database transactions (for up to 7 days), which can be used to reverse (undo) changes made to the database during that time period.

Therefore, your password change would probably be logged as something like “Database value in Field keyHash for User 85703 in Table UserData was changed from 8gYcnKGz+3ENJ9Ur2P1VfnFaE7wlyxJqtMNwi1gXqg4= to Fs91FR21uml1UkG+t0K1ryHu31gVz6oHE3fsenpVpjQ=”. It is not a given that an attacker would even be able to associate your old master password with any of your vault data, if the log files were compromised.