Have you tried disabling the setting -"continue running apps and extensions in the background when browser is closed"You should report this via Edge Settings > Feedback feature and you can include a screenshot automatically if you reproduce the YT bug. I sometimes repeat the bug report over time if it's an especially annoying bug that hasn't been fixed, e.g. on startup browser wasn't opening to selected pages.
One annoying bug that hasn't been fixed: browser hangs for 2-3 seconds upon closing.
Edit: This bug has been present since the introduction of Edge Chromium.