Update for anyone else searching regarding this issue in the future. I found a solution.
Credit goes to the user TiemenSch on reddit:
Had my Bluetooth adapter be undetected for some weeks now and could not for the life of me find a software solution. I just had to shutdown and fully unplug my desktop rig’s power (and held the power button some seconds afterwards fwiw, the internet told me to). After repowering and rebooting Bluetooth was re-enabled as if nothing ever happened. Did not think that would help at all in 2024, but here we are.