I know that for some of those services, you’ll need a premium account to access a site behind HTTP basic auth (Gtmetix)
Right now, there isn’t a way to disable the username/password for Live links, but you might upvote this feature request to get something like this worked on sooner:
I do have a couple of thoughts around measuring performance:
Most of those links are geared for measuring performance of Live sites that have been deployed on their target infrastructure. Running them against a site within Local over a Live Link might not give many useful things to follow up on since I imagine that they will have a slower TTFB given how your computer isn’t directly connected to the backbone of the internet.
For troubleshooting WordPress performance issues, I often recommend using the Query Monitor plugin: Query Monitor – WordPress plugin | WordPress.org It allows you to get detailed information about what kinds queries are being run in order to generate a page and can be a great way to start optimizing the backend processes that a site performs.