FINALLY, I got my S10 to update to Android 10.
If you read my previous posts, you'll see that I tried everything. I chatted with AT&T several times, chatted with Samsung, neither of which helped. My S10 was at the October security update which is old since Samsung updates every month. I finally tried something I read online: swap out the SIM card. I pulled the SIM card from my wife's iPad (AT&T) and put it in my S10 phone, and when I checked for software updates it started downloading an update! Since I haven't received any updates or patches since October, my phone had to download every patch sequentially, install it, and reboot the phone. So after several downloads and reboots, I finally got up to the December security patch with Android 10.
So, I definitely think my OTA update issues were tied to my SIM card. I'm going to visit my local AT&T store this weekend and see if they can swap it out for a new card so I don't have this issue in the future.