Advanced Key Fob Error Light - 2009 Mazda 6 GT

After leaving the dome light on for 2+ days, I got a jump on the completely drained battery. It took about 1 minute to get any power/lights in the car and then the car started. I should mention I had put the physical key in the steering column while this was ongoing and the advanced key fob was in the car as well. As soon as the car started the solid red key fob light appeared in the dash and the push start showed red as well but it still started and ran like normal. I drove it without any issue to charge the alternator.

From that point forward the key fob dash light shows solid red along with the start button BUT the key fob still seems to work exactly as before. It still unlocks the doors and the car still starts through the push button. The only apparent difference now is the the solid red key error light and the red light showing through the push start. It doesn't appear to be any sort of battery error in the key fob as I have new batteries in both of them. Any thoughts?