Red Triangle "Problem" - Low 12V Battery?

Hey everyone, so a couple of months ago our 2008 (100+k mi) Prius gave my wife the Red Triangle "Problem" while she was out and about with the kids running errands. It happened while she was at my office visiting me, so we switched cars and I let her take mine home while I gave our Prius a rest as I finished out the last half of my work day. I pretty much figured it was the inverter coolant pump since I had already previously replaced the coolant diverter valve that likes to get stuck and throw its own code. I got it home after work that day and pulled the codes with Techstream and it was the inverter pump as I thought so we replaced it and it was back to being a reliable family Prius again.

(I should also note, I recently replaced its HV battery as well with a good quality used pack from a reputable member here so I am confident no further issues should come from that.)

Fast forward some weeks/a few months and now I am working from home and our Prius gets even less driving time each week than it used to. One day, the whole family piled into the car and pretty much spent the entire day in the Prius running errands, traveling on the highway, through the city, idling in parking lots, with the A/C blasting on max cold the entire time in the dead of summer, etc. As we were nearing home we got the Red Triangle "Problem" again and our A/C stopped cooling. This time I had no clue what it could have been other than a possible air pocket in our cooling system or a weak 12V AUX battery. (We bought the Prius in California in late 2014 and have never changed the 12V battery out yet.)

A couple of weeks went by with it sitting in the driveway as I put off pulling codes due to needing to re-install Techstream again, and by the time I did go to pull codes last week, I realized the 12V battery was nearly dead after unlocking the car and sitting in it for a few minutes on ACC mode, not running. During that time it threw the "parking mechanism/pawl" warning which I am confident was purely from the low 12V battery. So naturally, I removed the 12V battery, freshened up all the connections and put it on a 2A smart trickle charger for about a day and a half until my charger gave me the "fully charged" indication at which point I put it back in the Prius and cleared all codes. I have driven it a few miles since and it did not immediately throw any new / major codes (besides its lifelong codes that I know it carries, but that don't illuminate the CEL).

Could a weak / failing 12V battery cause the Red Triangle "Problem" issue to occur randomly / intermittently? If so, does the Prius just always elliminate the air conditioning whenever the Red Triangle gets thrown? Should I be concerned my inverter, A/C compressor, or transmission could be on their way out?

EDIT:
Also, after installing the re-charged 12V battery, I was getting 11.9V (via Techstream) while in ACC mode with nothing on, and 11.3V with A/C and headlights on. Also, while sitting in the driveway with the A/C on high MAX COLD as I was pulling codes with our Prius idling, I noticed a metallic tapping sound, but not from our engine. I turned the A/C off and it stopped. So that has me wondering if any of this could be related to a failing air conditioner compressor... Except for the fact that our Prius's A/C is ice cold and operating within tolerances as far as its cooling ability goes.

 

The HV pack I had replaced recently is a rebuilt pack from a wrecked 2015 that had 30k mi on it. New wiring harness, cells charged and tested prior to rebuilding, etc. It's really pretty low on my list of suspects.

 

I did just pick up a NOCO Genius 5 charger since my "old-school" (transformer-style) Schumacher digital with microprocessor charger stopped working right after getting my Prius' 12V fully charged. (I never did like/fully trust that charger for some reason, lol) I trust the NOCO way more and it even has a "repair" mode to help de-sulfate older batteries. I figured it can't hurt to try while I decide on my replacement 12V battery setup.

 

The 2015 wrecked Prius the HV pack came out of only had 30k miles on it. We bought it and installed it into our 2008 Prius in August 2019 about a year ago. Our Prius is not our primary commuter anymore since I got a 2005 Corolla, and our Prius gets driven even less since March with the pandemic and everything. I doubt we have even put 5 to 10k miles on the HV pack in the year we have had it in our Prius.