I have exactly the same issue. My battery had 16 cycles on a day I did upgrade to Big Sur. Following the upgrade it ran an optimalization for battery and lo an behold - battery needs servicing. Tried resetting all of the settings and PV and SMC but nothing so far helped. Even clean install didn't help. Clearly there is something wrong with software side of things or this is a very unlucky coincidence.

Additional observation - due to battery issue my CPU is limited to 1,5GHz....

So it seems like we have at least identified one walk-around. Downgrade (fresh install) of Catalina. I will do this today and confirm if it worked for me. Regardless, this further indicates we have an issue with Big Sur rather than hardware. Keeping in mind some people might in fact need their batteries replaced. I just wonder why Apple is not recognizing this nor issued a patch. I strongly believe Apple has much better knowlegde about the root cause than we. So either this is limited to too small number of cases or it is not that trivial to fix.

Update from my side. No bueno. Downgraded to Catalina and still the same issue. Battery with 19 cycles is considered broken.

Ok. Update from my side. Apple replaced my top case (battery plus touchpad) for free. Service recall apparently.