I'm struggling with this too atm but a clue that might nudge someone:
Deleting the shortcut to Kate in
~/.local/share/applications/ resolved this issue completely for me (inc. restoring it in favorites etc).
The problem is, the next time you start Kate, it just recreates that file and makes the shortcuts disappear again!
Seems like a conflict but that is as far as I've managed to come so far.
Update: purged Kate using apt, manually deleted the offending shortcuts, reinstalled Kate using Ubuntu Software GUI instead and now this problem is gone?! instead my custom syntax definitions don't work like they used to now but that'd be outside context.