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:
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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.
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In the case of Google’s page speed test, there are ways to run it locally so that you can find the issues that the hosted service would give you. See this StackOverflow question for more thoughts: web testing - Can I use pagespeed insights for my local host website or offline? - Stack Overflow
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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.