Trying to install from scratch doesn’t even work, it just refuses to install the game. Renaming or trying to install to a different folder/drive also doesn’t seem to work. Running BattleNet as an admin.
EDIT: Renaming your SC2 folder in “C:\Users\Name\Documents\StarCraft II” To something else allows you to update/install. Just make sure to backup your replays and hotkeys.
Replays can never be restored without recreating the problem, but you can still watch and share them if you launch them outside of SC2. Hotkeys and Variables profiles can be restored without any problems.
You will still have a problem with renaming or deleting new replays that are created when you play, this can be resolved by taking control of the replays folder.
Huge mess fixing something that shouldn’t be a problem in the first place. Goodluck.