Car keeps losing charge seemingly randomly with new FSR and voltage regulator

[YoitsTmac]

Experiencing some wild issues when it comes to my battery. Here's my quick history. Three times in the last 60 days, my battery has depleted so low that I was unable to start the car. The first time I thought it was a fluke, and the second time I decided to do something about it. I bought a new FSR (Rein from FCP), new Voltage Regulator and a new-to-me HVAC control unit. March 30th I drove to work and turned off my car, to find the HVAC still on. I could even completely lock my car and unlock my car and the HVAC control panel stayed on until I unplugged my battery.

Some time in the last 7 days, my HVAC unit randomly changed to Celsius. No amount of driving, on-off cycling or deep sleep states corrected this behavior. Saturday I was unable to use my HVAC controls at all, a previous symptom I have experienced. I got home, unplugged the battery, reconnect it, and my HVAC has returned to Fahrenheit and now turned on.

Sunday came around and I was growing concerned. In the middle of day, my battery is reported 12.4V according to my radar, tapped into the power of my mirror. Monday morning came along and the car unlocked, but refused to crank at all. Radar reported 9.4V. I disconnected the battery. When I got home from work in another vehicle, the battery was reporting 10.8V. Seeing that, I went to get my battery charged back up to 12.4V. I left it unplugged overnight, drove it to work today (Tuesday), unplugged it at work, and then got the battery tested. Previously they would indicate to me the battery is healthy but needs charge, however this time they said it seemed charge. Today I got home and it reported 12.2V.

I want to believe that the battery issue is unrelated to the HVAC system, but the fact that the HVAC stayed on after I turned the car off even with a new FSR leads me to believe its still an issue in this system. I went just went down to the car for this post. The voltage is 12.2V right now, and I have a shadow code in the HVAC for "Auxillary heater Relay" aka the K4 relay. I want to believe the relay is sticky, but that would be just for the heater as far as I can see, not for the entire climate control panel. This thread seems to believe otherwise. PN is 61 36 8 373 700. I'm not sure what to do from here, but any advice is appreciated.

Edit: The wiring diagram does imply that power predominately comes through fuse 37, 28 with the latter also powering the FSU.

edit 2: except for the 30 seconds of running right after the freshly charged battery was in, the car is stuck at 13.5V when running regardless of battery charge state.