iPhone SE restart loop when battery gets below certain percentage

Hello,

I have an iPhone SE, 128GB and when it gets below 30% it will randomly restart, and when it comes back on it will say the battery is at around 1% or so. Then it will reboot again and say it is at another percentage, it will eventually just turn off completely. It has done this with both iOS 12 and 13. Also, when it charges sometimes it will vibrate when it is at 100% (this is not because of notifications or anything like that).

Here are the steps I have attempted to try to resolve this issue;

1) I only use official Apple cables and power adapters, so I have tried various different ones.

2) Charging the battery fully and letting it drain on its own until it will not turn back on, then fully charging it again (I did this about 6 different times).

3) A full DFU restore.

The odd thing is, if I do not use it, the phone will naturally go down to zero (over an expected time). The battery will actually last an amazingly long time. However, if I multitask, it will do this restart loop. The odd thing is when it comes back on the battery will be at a completely random level.

Also, I checked the battery health and it says that it is at 99%. This phone is covered with Apple Care until July 2020. The Apple store is about 3 hour round trip from my location. Does this sound like a hardware issue? I just want to make sure that it is worth the drive.

I also wanted to add that it has no water damage (I checked the moisture indicators). The phone is almost in mint condition.

Thanks for your time.