Microsoft has some decent documentation on debugging Content Scripts for an Edge Extension and the top of the page even includes a Channel 9 video on the subject.
Unfortunately, the techniques no longer seem to work, as even when following the debug instructions and using the the sample Text Swap extension, the extension and content script never show up in the debugger.
As you can see from the screenshot, the content script has run (and changed the font on the page) but it and the extension itself are nowhere to be seen in the debugger.
Anyone figured out how to get the content script to show up in the debugger?