Well, unless there is zero integration with the browser, then it’s just a matter of time before some exploit will expose how to retrieve arbitrary information from the external tool.

And of course, the external tool can have plenty of exploitable leaks unrelated to whether or not it’s integrated to some browser.

If the goal is to have better security, no method of using password alone will bring significant improvement to an authentication system, no matter how great the password manager it’s used with.