Closes https://github.com/ppy/osu/issues/17965.
Note that this will cause a second osu! icon to appear after running the
application (after any update). As per the inline comment, this will
eventually be resolved via https://github.com/clowd/Clowd.Squirrel/issues/24.
I do think having context menus working is more important than duplicate
icons.
Note that for anyone who already has a pinned taskbar icon, it will need
to be manually unpinned and repinned after a future update to actually
fix this issue.
Thanks to @caesay for help with investigation.