iPhone SE 128GB problem with battery?

Bought an SE with a cracked screen on Craiglist. Phone was fully working. I purchased a replacement screen. I put the new screen on and everything was fine for ~30m. I come back to it after dinner, and colors are messed up and there's already burn in on the screen (burn in of the home screen). The phone started randomly shutting down and would report 1% battery life on startup and whenever plugged in. I installed a known good display and my color issue was fixed, but the other symptoms remain. Whenever I unplug it, it reports the correct battery percentage (12 percent, currently) but then force restarts shortly after. I bought a replacement battery, but the same symptoms were present with the new battery plugged in. Battery health says that the phone battery needs to be 'serviced' with both batteries, one of which had a reported 90% life before this whole ordeal. How to resolve it?