Passwords need to be sent both with the request, and to the requestor. I think GP is referring to sending credentials to the service making the request.
It is far better to give service XYZ a time-bound and scope limited token to perform a request than a user's username and password.
Chromium removed support for generating TLS Client Certs within chrome in 2016 [0] and ever since then it has gotten harder and harder to use mTLS in Chrome/Chromium. Ten years ago it wasn't a great UX, but now it isn't even obvious how to use it. The impression I've gotten is that Chrome isn't interested mTLS.