Actually, Bitwarden does have its own Watchtower alternative; you'd access Data Breach Report in the menu, and it tells you which accounts need their passwords changed. I'm not sure if it sends a notification when a new breach comes in that includes your account.

Have I Been Pwned partnered directly with 1Password, which is probably why they're able to send out notifications directly; Bitwarden has to worry about being rate-limited.

I'm not too sure what's meant by MFA availability, but Bitwarden also lets you use it as a TOTP generator + use 2FA for logging into your vault, though those are premium features.