You're definitely behind on software updates, FSD aside. This is a little strange and brings up the question of whether your car is getting any Wi-Fi connectivity. Also check that your smartphone Tesla app is up to date.
For FSD beta (assuming you bought FSD capability or subscribed to it) the first thing you need to do is to get on the 2022.44 x branch if possible. From there you can request and receive FSD beta within a day or two. You'll he told you have to qualify with the slSafety Score, and it will temporarily appear in your app while you're waiting, but you actually don't need to worry about it as there is no longer a minimum-score threshold. I do think you need to have >100 miles of recent driving on regular Autopilot though.
What you don't want is to upgrade to the 2023.2.x branch, because there isn't yet an available FSD beta release on that branch, and they won't down-version you to give you FSD beta.
So if you're on 2022.40.x now, I think you should make sure you have requested FSD beta and answered the associated agreements. Then go to the Software menu and scroll down to Check for Updates. If you see any version of 2022 44.x, go ahead and take it. It will either contain FSD beta or be able to bridge to it upon request.
But if you see 2023. 2.x do not install it. Try to keep deferring that install by scheduling it later. This advice could change, if and when they release a version of that branch that does include FSD beta. For most of 2022, the FSD beta users were one or two versions behind, but there was a golden period around Christmastime when the 2022.44 Holiday Update synchronized with the "wide" FSD beta release, meaning that people with the latest regular software could easily jump to FSD beta. Unfortunately it seems like your car never got the holiday update, so now you have to fend off non-FSDb updates that would
If you don't see any availability, and if you changed anything that could make a difference, wait another couple of days. If still nothing happens, and/or if you think you already followed all of the other advice, then there's something going on that's preventing your car from normal updating. In that case you might need to talk to Tesla Service, but again be careful about ending up with 2023.2.x. Based on comments here on the Flforum, it seems the service people aren't always tuned in to the details FSD beta software versioning issues.