This requires you to save your password in your Google account which sounds like a bad idea from both privacy and security standpoints. Google has proven many times that they can't be trusted with personal data, and you also create more surface for attackers who'd want to compromise your accounts - instead of just one device, all of your devices that are connected to Google could be used to steal your passwords.
Alternatively, you can also use
https://haveibeenpwned.com/They even have a notification service whereas you would be notified if one of the websites your certain email is registered on is hacked/compromised, so you can change your password on that website as soon as possible to prevent problems with your account.
Haveibeenpwned
uses cryptography to guarantee users that they don't collect their submitted plaintext passwords - but we don't know how passwords.google.com works, and if they give us any guarantees, so it's better to avoid it.