Today youtube videos and playlist tabs stopped working for me in all channels. I've tried it both on Chrome (logged in) and Firefox (not logged in). Both times the panel just turns blank when trying to access the videos or playlist tabs in the channel.
The only workaround I've found is to remove /c from the URL. My URL looked like this:
https://www.youtube.com/c/[channel]/videos
When I remove the /c from the URL it shows the videos correctly. I am surprised this issue has not received more complaints. I think it is something do with the google account because when not signed in, videos load normally for me, when signed in I get the exact same issue as you have shown above. I have not found the problem mentioned anywhere else on my google search. It is a difficult problem to find help with because there are so many similar results when using the keywords blank youtube channel videos. I see what you mean when the /user part is in the url there is no /c to remove so the workaround doesn't help you there.