I may be wrong, but my understanding is that 8bitdo controllers do have gyro, but specifically for Switch mode. Most of their switch compatible controllers have a relatively easy way to swap to it and connect via Bluetooth. Unfortunately that does mean no analogue triggers though

The 8bitdo Pro 2 does not have Hall effect sticks afaik. The only 8bitdo controller that does as of now is the Ultimate Bluetooth model (not the 2.4ghz or wired).