Software update HELP!

Is it an AT&T branded phone? 

Well I bought the phone through At&t in an installment plan so I'd guess yes? It's a locked device but I don't see any physical branding on the device just on the display.

I'm having the same issue. I have the Note 20 Ultra and have not received a software update since July 1.

Unfortunately, it seems that you are among the small but not insignificant group of AT&T customers that have had their phone lost to the AT&T OS update servers.  This has been going on for a number of years now (at least since the S8 days, maybe longer).  There have been many complaints about it on these forums and elsewhere, but AT&T still can't seem to fix it.

Our best guess - those of us who don't work for AT&T, are just other customers, but try to help the best we can - is that somehow the IMEI of your phone gets lost or disconnected from your account in the update back-end server system.  You can speak to Customer Service all day long, and even up the Tech Support chain, and they will see your phone just fine. But no amount of "we will push the update to you" ever seems to work if it couldn't do it on its own. 

To make matters worse, most of the time, even updating to a new phone doesn't seem to help - probably because the updated phone passes from the old IMEI to the new IMEI, and it seems that if the previous IMEI couldn't be seen by the update servers, then the new one isn't seen either.  Again, this is just a guess. 

The only way to really update is to do it yourself.  While specific AT&T versions of the OS are not available as you noted, Samsung OS files are really universal with only a few needed support files to include.  AT&T will generally insert their own modified settings into the system once you are on their network (like locking out the ability to set the mobile network type you want to use).  I'd check out the Android Central Forums.  There are users over there that can help with how to find the right firmware to start with.