Bachi I've just experienced a bootloop this morning. The pixel 8a would boot immediately after plugging in the charger and it would shut down immedaitely on the sim unlock screen due to too low of a battery. This despite using a fast charger. I had to interrupt the boot process at the 'loading different OS' warning screen by pressing the power button once, waiting for a while and pressing it again. Maybe give it a try?
As for random battery percentage fall, I know nothing about it and so far haven't experienced it myself.