Cursor jumping around on MB Pro, but only when connected to power adapter.

I have a new 2020 13" MacBook Pro and noticed charging issues from the beginning; I used the power adapter that came in the box (USB-C) and noticed that even though it was plugged in and the charging icon appeared in the Menu Bar, the charge still was going down. I used different outlets with mixed results (sometimes it worked, sometimes it didn't). At the moment, this issue no longer occurs.

The more recent issue I've been having which I suspect comes from some problem with the battery is the fact that when my MacBook Pro is connected to power, the cursor has a tendency to jump around when I let it go (usually jumps around up-down by ~6 pixels). When I unplug the adapter, the problem stops.

I tried resetting the SMC, reinstalling the OS, and I even backed up my files and wiped the disk to see if it was some kind of software issue, but it still persists. Is there anything I can do? Is there a chance this is a result of a defective battery?

I have not used any Bluetooth devices (I had BT turned off).