I’ve got a Pi 4 2GB model and believe I’m having the same problem as you. The hardware on board is an even older revision:
Hardware : BCM2711
Revision : b03114
Serial : xxx
Model : Raspberry Pi 4 Model B Rev 1.4
I’m starting to suspect that the hardware is bugged or the drivers incompatible. I’ve tried a lot in my own topic at Pi 4 Bluetooth not working, Sap driver failed , although granted it’s in Raspberry Pi OS and not Retropie. If it truly is a bug, should we file it more directly towards the Raspberry Pi devs?
Edit: Here’s a post on the Raspberry Pi forums: RPi4 Bluetooth woes - Raspberry Pi Forums
This is a known issue and they have a fix deployed, however it wasn’t added to the apt for some reason. This is for the 8GB model, however.