Not really a solution, but here is what happened. Before I begin, I'd like to say that, after my original post, I submitted FB9103124 to Apple on May 11, but there has been no response. Sadly, here we are. Support requests have begun to come in from my users also. There are actually two issues. Full Disk Access is summarily disabled for all non-Apple apps which previously had it enabled. Helper Tool no longer inherits Full Disk Access from parent app. Issue (1) is of course, just very annoying to users who must visit our web pages or email us to find what the @%*#! happened, and we need to apologize on behalf of Apple. Issue (2) kind of went away by itself for me. It may have been that I had two useable versions of my app on my computer. After deleting one of them, and restarting a couple times, the remaining the FooAgent had Full Disk Access again, and eventually its inexplicable checkbox in System Preferences Security & Privacy Full Disk Access disappeared. I may have a few users with the more serious issue (2), so I'm just telling them to look for other versions, restart, etc. Yes, it is a sad day here for the Mac.

I found the problem. I forgot that I had Audio Hijack (software by Rogue Amoeba) installed, and I had not used it in a month or so. So I launched Audio Hijack, after about 10 minutes of beachballing, a dialog advised me that I had version 3.8.0 and needed an "Urgent" update to 3.8.3. After doing so, and further following the prompts to install Rogue Amoeba's new Audio Capture Engine (ACE) system extension (or whatever it is) that comes along with Audio Hijack, the problem is solved. Apparently the old ACE was the cause. Thanks for the quick fix, Rogue Amoeba!