I didn't even notice that there _was_ a testing framework, which uses a 'special' SL account to log in, etc. Sadly, the way the login information is passed to GitHub Actions is anything but obvious; as such, this will be my last experiment — I'll skip the testing part if this doesn't work. After all, AppVeyor will run all the tests properly...
Due to an intermediate merger with upstream code, I lost my .editorconfig configuration; this meant that new YAML files were included with TABs, not the required spaces (arrrgh!!) and that required manual fixing, too.
I also restored .editorconfig and tweaked it to guarantee uniformity in spaces/indents — this might be useful for others running editors/IDEs that comply with .editorconfig (and even GitHub will comply with the .editorconfig rules when editing files online!)
On a different project, adding the dotnet.yml framework and specifying a version of .NET to run (6.0.X in this case) managed to get the automated scripts to finish with success. Let's see if the same 'magic' happens here.