Not the completely right forum. There is no forum for the questions about the VLC website or some of the parts of it, like code or wiki. So I had the same issue you got (need the 2FA, but don't like to install another software or sign-up for another service), looked in the forum and found nothing. Then I found a solution and posted it here. Just because this solution has something to do with some Linux program doesn't mean I have to post it on the Linux forum. At the end, I don't have a problem with VLC itself on Linux, and this is what that forum for.
As for WinAuth it only supports the following sites: Google, Microsoft, Net, Guild Wars 2, Glyph/Trion and Steam. If you're going to recommend a tool please test it yourself first otherwise you're just wasting people's time.
WinAuth supports as a first item in the add menu some generic authenticator. And this is what we are having here. The services you are listed are just some specific extras. Of course, I tested it before I recommended it. If one like, one can even go to the end: create a database in WinAuth and generate a PIN every time one sign-in to the GitLab on VLC.
I even tested WinAuth on Linux (with wine) and it works here too. Both scenarios: generate the PIN every time and deactivate 2FA afterwards, or generate the WinAuth's database and just let the PIN been created every time one needs it.