At first, I thought that this issue was fixed in macOS 11.5 Beta, because my background agent was getting Full Disk Access without being listed in System Preferences' Full Disk Access list. But, then, and I don't know what I did other than build another new version of my app the other day with Xcode, my helper lost Full Disk Access. Actually, it is even worse than before, because now throwing the kitchen sink at the Apple does not fix it on my Mac.
Also, I have had two users report that throwing the kitchen sink at the Apple does not fix it for them, although, for dozens of users, either just re-enabling Full Disk Access for the parent app, throwing the kitchen sink at the Apple does seem to fix the problem. Mercifully, so far, my computer is the only one which has reportedly had the issue recur after it was "fixed". But I can imagine all hell breaking loose worse this time if Apple releases macOS 11.5 without fixing this, or at least telling developers what they need to change in their apps to make them work again.