I've tried several Bluetooth 5.3 transmitters currently sold on Amazon, and I couldn't get any of them to reliably work with the AirPods Pro 2nd Gen. I was able to get one to work after factory resetting the AirPods and pairing to the transmitter before pairing with an Apple device, but after I paired with an Apple device, I no longer got audio with the transmitter.
I decided to dig out an old TaoTronics TT-BA07 with Bluetooth 5.0 that I stopped using, since the transmitter doesn't have volume buttons, so the sound was too quiet with my older AirPods, which don't have volume control either. Ironically, the transmitter works fine with my AirPods Pro 2nd Gen. And since those AirPods support volume control by sliding up and down on the stem, I think the transmitter's lack of volume control won't be an issue.
All of the ones from Amazon that I found to be incompatible were newer models using Bluetooth 5.2 or 5.3, which I thought would work well, since the AirPods Pro 2nd Gen also supports 5.3. However, it appears that the older transmitters with Bluetooth 5.0 or with older chipsets may be the answer. I bet that has something to do with why the newer AirFly 2nd Gen is not not compatible.