Reading and following this Steam Forum page: https://steamcommunity.com/sharedfiles/filedetails/?id=3150369779

skimmed through this one also: https://steamcommunity.com/app/353370/discussions/1/6516193260178656983/?ctp=13

Installing BLE Update

Need to use an older version of Steam. Best option is to download a version of Steam for Windows.

Link from someone in the community: https://mega.nz/file/OnZQSKjL#xZP0qBz7fxT3vx39GeCGaj89V6H2rmhD4xxRu1RGej4

Updating the Firmware:

Some windows tool to update the firmware.

(It may be possible to do it just through any OS by mounting the Steam Controller by holding Right Trigger while connecting through USB cable)