Power issues while resurrecting the dead. Battery?

Got an iPhone 8 Plus that was run over by a car. Yeah, really. Screen is shattered but surprisingly still functional. Back glass is cracked in many places. Opened it up and a bit of water came out; I also found three tripped moisture sensors.

I pulled the battery and put the phone in the dehydrator for awhile. Hooked up a replacement screen, did a factory restore, and it’s working. It sees wifi and 4G, the home button and Touch ID works, all the buttons work, it charges, iTunes sees it when connected to a PC, etc.

Issues.

1. The phone is caught in a sort of modified boot loop. It starts up and gets to the home screen. If you do nothing, after maybe 10-20 seconds the phone reboots all by itself and the cycle repeats. But (interestingly) if you start using the phone, it stays active/normal all while you use it. It will never spontaneously reboot while you’re using it, but once you stop using it, the phone will eventually dim the screen and go into auto-lock — except instead of auto-lock, it reboots.
2. The battery gets warm-to-very-warm while plugged in, but it does charge. Right now it’s at about 50% capacity after charging for a couple of hours. The iOS “battery health” function in Settings says the battery has 99% of its life remaining. (The phone is <4 months old.)
3. With the phone is turned off and plugged into a charger, if you unplug the battery from the mobo it won’t boot. In the same scenario with the phone turned on, the phone will immediately shut off; it won’t run off the charger.

I am, alas, out of spare 8 Plus batteries until Thursday so I can’t test that. Could it be something other than a bad battery?

EDIT: With the charger unplugged (running on battery only), the phone gets very warm/hot to the touch just below the camera.