Chosen Solution
I replaced my battery with an aftermarket replacement while running Mojave OS. I went through the initial calibration - fully charging the battery for two hours and then using it until shutdown. After that I used my computer for an hour or so, shut it for the night (unplugged), and in the morning the battery was drained. I put the charger in and downloaded CoconutBattery. This divulged that my computer woke in the night and rapidly drained the battery for no apparent reason. Shortly after this, the battery icon disappeared and CoconutBattery could no longer detect the battery. I reset SMP and PRAM. I upgraded the OS to Monterrey. Still not registering the battery. I have since replaced my old and failing battery, which registers just fine. Is my “new” replacement battery simply a dud?
If going back to your old battery solved the issue of it registering, then it absolutely sounds like the new battery may have defects of some sort, but if you just bought it, you should have no issue returning it or swapping it for a new one.