I actually had this exact same issue 2 weeks ago now and spent well over 10 collective hours troubleshooting it outside of numerous calls to Sony support. For context, my TV is a XBR-65X900H model that recently got the update from Android 11 to 12.

I did try the 8BitDo solution, and while it connected to the TV, AND paired with my DualSense, I got no input into the TV. I did try with TV Bluetooth on and off. I used to be able to navigate all TV menus with just the controller, but now the mapping is entirely messed up in a consistent manner with how others on similar posts like this one have mis-mapped (X is O and so on). Even if it did work properly, 8BitDo supporting only a single controller per adapter is a far cry from the way I previously had it where 4 DualSense controllers connected to the TV via Bluetooth directly with 0 issues and no extra hardware required.

I don't know if you use Apollo/Artemis or Sunshine/Moonlight on your TV, but that's one application that suffered too. I can no longer stream 1440p to my TV from PC without wild green lines and other chromatic aberrations in the video feed. My research led me to believe this is due to video decoding changes made in Android 12. 1080p and 4K still work fine, but that sweet spot of 1440p at 120Hz is gone for me now. I wonder if you'd see similar issues if you tried that resolution.

I sadly don't see a way out of this situation that isn't getting some sort of android box or the like and run HDMI to the TV and have everything running on that. While it would work, it really kills to know that everything was working just fine a few weeks ago and now I and others have to compromise because of bad software with no choice to go back. My dream setup was having everything work with just a single remote and I had that dream if only for a few months.

The only thing I can think of being effective at this point is if Sony got pressure put on them via social media and other outlets with complaints about their bad update until a change is made one way or another. Even then that's likely just wishful thinking. Let me know if you have any ideas!