I experienced this issue again, so I tried to use the New Bing AI Chat experience to solve it and made some headway. Here were it's suggestions:
This error may occur when you run a desktop flow that has a "Launch Edge" action in Microsoft Power Automate (learn.microsoft.com). It could be caused by one of these reasons:
• The web extension is not installed properly or enabled (learn.microsoft.com).
• The browser is not running when the action is executed (learn.microsoft.com).
• The browser is running in private mode (learn.microsoft.com).
• The browser has multiple tabs or windows open (powerusers.microsoft.com).
To fix this error, you can try these steps:
• Make sure the web extension is installed and enabled for Microsoft Edge (learn.microsoft.com).
• Make sure the browser is running before executing the action (learn.microsoft.com).
• Make sure the browser is not running in private mode (learn.microsoft.com).
• Close any other tabs or windows that are not related to the flow (powerusers.microsoft.com).
After trying this and none of it working, I verified the URL from my flow and found that it was valid, but not the URL I had anticipated.
In order to get it to launch, I had to have the browser open and on the specific page listed in the flow - then the flow was able to execute. I was expecting to be able to run the flow, have it open a browser, then navigate to the URL specified.
So, if you get the same error, maybe one of the steps above will help, or maybe you need to have the browser open and on the specified page for it to function as was my case.