I got mine working. The connector to the gateway requires your local user account's login credentials.
It's confusing because the gateway settings references some PBI (Power BI) something or other credential, but that is not what you use for the gateway connector in Power Automate. The PBI thing I am talking about is some pseudo-account-credential looking thing that has like PBISE or some such letter sequence in what would be the username. I was confused by this and thought it might be some auto generated login credential, like API keys. I even tried establishing the gateway connector using that thing, but that was not correct to do. You must use credentials of local user account where the gate way is installed.
Part of my problem is that Hyper-V Windows 10 virtual machines do not have a local account password for the default user account within the virtual machine. Or that default user account logs itself in anyway, so I was not sure how to find its password. So I made a second local user account within my VM and used its credentials for the PAD gateway connector in the Power Automate cloud flow run. I just log in as my second local user, then Power Automate and the gateway do the rest. Look out for the two PAD taskbar icons wherever you install the gateway and intend to run your cloud-triggered PAD flows. If you have the taskbar icons showing up, you are probably good to go on the desktop side of the equation. Then it's just a matter of using the local user account's login credentials to authenticate the PAD cloud action connector to your gateway.
Ask me specific questions and maybe I can help you.
EDIT: That user account credential looking crap is NT Service\PBIEgwService (as in Power Business Intelligence Gateway Service), and you will see it referenced several times whenever you set up your gateway. DO NOT USE THAT TO AUTHENTICATE YOUR CONNECTOR - it won't work. That credential is, I'm guessing, what authorizes the gateway to do its bidding on your PC. Use the local user account like [Name of Computer]\[Username] e.g. My-PC\TurdFerguson. If you don't login with local credentials e.g. you login with your Microsoft account, you will need to make a local user account to set up your gateway and run cloud flows on it. Or I do not know of a workaround to do it without local user account credentials anyway. Ok thanks for coming to my TedTalk 🙋♂️