Check the BMS sensor for corrosion. (Connector & sensor body) Also check that the white wire leading from the red battery terminal doesn't have any corrosion as thus powers the BMS sensor.
With the vehicle at Idle measure voltage at the battery. Should be around 14 VDC.
Yes if the AGS (or alternator) connectors have moisture trapped this can also cause a battery light to trigger.
The components you added did not cause this to happen.
I believe that a 96R is the correct size battery. If you switch size or styles the PCM must be updated to reflect this change
The "Battery Light" came back on again for awhile yesterday for awhile. When it does- there is no detectable change in the way the car operates, and it runs and drives as it should. Another interesting occurrence also happened: at cold startup (after the car sat for ~3hours while I was at my night job) I turned the car on, and it started up normally- but the center screen (ST3) was solid blue for a second- then a warning popped up stating that the rear camera is either not available or not connected. This confirms to me that there is definitely something going on with this car. I recently hardwired a dashcam and drove the car for a week without any issues or problems, then installed a new battery, and the car worked perfectly fine for another few weeks before I saw a battery light warning, and now this odd center screen behavior. I read through the "Key Not Detected" thread, and it was very interesting, but did not yield a resolution in my specific case.
I know you stated that my hardwiring has nothing to do with any of this- but I am considering unplugging the add-a-fuse connected to F85 (and inserting the fuse as when stock) to see if that has any effect. Fuse 85 is stated as follows in the Owners Manual:
I'm wondering what "voltage quality monitoring" is, and if I have a constant draw on that circuit- (used for my dash cam "Parking Mode") if it's causing these problems.
For the record- I wanted/intended on utilizing F61 as you suggested in your masterful writeup about adding fuse taps, but F61 is right up against a large connector, which prevents an Add-a-Fuse from fitting. Is there a different type of mini Add-a-Fuse that would work in F61?