@NZ00Z3 is spot on, the F0 code onb the module locks up the module and prevents codes being cleared, it is what they call crash data sitting in the eeprom chip on the units internal pcb that is the cause. I had a conversation with the guy in Houston who posted the linked thread on bimmerforums when sorting a mates problem with his airbag module. He would have fixed it if it was posted to him. Further digging with my mates problem actually disclosed that he had replaced what he found on his car with a same part number module from ebay, when I got involved I discovered it and the one he took out of the car was in fact the wrong part number module for his car. The replacement was also locked up showing both pretensioner codes present which indicated the module had come from a crashed car and was locked up with crash data in the eeprom. Ther are firms who offer a crash data removal service at a cost, circa £130+, google search should find them.
Alternative is to source a used module with the same part number as your original and fit that, it will require coding to your car which can be done with INPA and NCS Expert software. Bit of a lottery buying from ebay, they may have come from crashed cars and have the exact same code as yours has and you would be back at square one. I sourced a known good module from our resident breaker
@spurs fan in a coupe who knew the car it came from was not a crashed car and had no airbag light on when the car was broken for spares. Fitted that and coded it to the car and we were back in business with no airbag light.
There is software available that will read eeprom chips and allow the crash data to be cleaned from the chips, its not cheap and requires the chip to be removed from the pcb in order to read it and process the resulting .bin file. Once the crash data is removed the cleaned .bin file has to be written back to the eeprom chip and that resoldered to the pcb. All this interests me so currently collecting the software and pcb soldering kit to have a go at clearing these F0 faulted modules but not yet in a position to have a go yet.
If you find a correct part numbered module for your car fit that and find someone on here close to you who could code it to your car, its a pain to get the module out but doable with a small spanner and reaching through the drivers footwell with the centre console side panel pulled back. Probably best access with the seat out, all done with the battery disconnected.
Explanation on NCS Expert coding here
https://www.ebay.co.uk/itm/143398094509?hash=item21633146ad:g:hbIAAOSw8YddjIHp
Refers to comfort access coding but shows how modules are coded.