You don’t need to redownload it. Go into the XBox app to FH5, find manage in the menu. There you should find a large “Activate advanced management” button. Use that to move the game from the old Windows Apps installation folder to the new XBox games one.
It is a copy and then delete unfortunately, so you need to have about 120 GB free disk space for it to work.
Same thing for Halo Infinite btw.
Example of the button (already used it for FH5):
