To answer your early question, DoD guidance was to give medical exemptions to those that had a serological antibody test done for previous infections. I linked it earlier in the thread, but here it is again:
Exemption Guidance for immunizations
health.mil
I believe that guidance is from 2019. So whatever quality of test they had was good enough for every other vaccine and infection for the military. Since we know natural immunization is stronger and lasts longer than vaccination, we should have no reason to put covid under a different umbrella.
But alas, SECDEF has said previous infection does not count as fully vaccinated (duh, it's fixing better than), I wouldn't be surprised if that's alluding to also not granting exemptions for it.
Might be an interesting January for me. At least 27 Chair Force pilots are leading by example with their commissions.