There have been cases where the battery voltage became quite variable before there were clearly visible symptoms. If you see weird patterns in your battery stats (here’s one example from a topic with many), then there may be an issue with the battery. I’m not sure what the warranty is on the replacement batteries, but it could be a warranty issue if there is a problem with the battery.
The reason for asking about the SIM is that a defective SIM can sometimes wreak havoc on the phone as well. If you get stuck in another loop, try removing the battery and the SIM, and then replacing only the battery. Normally I’d expect other symptoms as well, but misbehaving SIM issues are generally weird.
It’s difficult to troubleshoot not-very-reproducible issues like these, not sure what else to try at this stage…