Hi jkeXZ,
Thank you for reaching out Microsoft Community. We're sorry for the delayed response.
Have you tried uninstalling/reinstalling the Youtube app itself? If you haven't done that, you may uninstall/reinstall the app and check if this makes any changes. Aside from doing that, have you tried pressing CTRL button the keyboard to open other videos in new tab? How about right-clicking the video to see options like "open in new tab "? You can also run the Surface Diagnostic Toolkit to fix some of the common issues that may happen on your Surface device.
Kind Regards,
Crest