I think that ignoring security warning desensitize you to them, so that if your situations become real, there is a good chance that you might ignore them, so it's best to take actions to mitigate the situation, real or imaginary.
Report of a password leak: change the passwords for accounts that you use this password everywhere. There are plenty of password generators out there; use a randomly generated password. Use a unique password for each account. Use a password book/password manager to help remembering the passwords. Typically, if you use a random password/passphrase generator, and the generated password is long enough, you would never hear such a warning from Google again. If your account provider has a breach, unless they store the passwords in plaintext, your password isn't likely leaked (and it doesn't get reused on other services anyway), you might just have to change password for one service.