12 volt Battery issues

So I’ve had my NX 450H + since March of 2022 and for the most part love it….but this past week as I was washing and waxing it in my driveway and had it in “Auxiliary mode“ and the radio on for approximately 20 minutes the SUV started going bezerk …lights flashing, doors wouldn’t open….nothing working properly…information on the dash told me to take to dealer right away…

So called “Lexus road side assist” and they sent a tow truck right away…the tow truck driver decided to try and boost the 12 volt battery to see if this was the problem…but just getting access to the rear hatch was challenging…
had to first use the “boost contact point” under the hood…( see owners manual) …then we were able to open rear hatch to access the 12 volt battery…
we then boosted the 12 volt battery and within 5 minutes we were able to get a “ready light”
but information on dash still told me to take to dealer ASAP as the check engine light was illuminate.

took to dealer who ran diagnostics and they confirmed the 12 volt battery indeed had experienced low voltage and caused a few error codes…

they then told me I needed to run the gasoline engine more often to charge the 12 volt battery as I basically never run in hybrid mode but 95 % in EV mode..

I then asked them if the 12 volt battery charged while in EV mode or when the vehicle was plugged into AC…their response was no it did not…

well I didn’t believe them and researched the RAVE 4 Prime plug-in Hybrid which is exactly the same running gear as my Lexus and on their forum it indicates it actually does charge the 12 Volt battery when plugged in to AC or when in EV mode…

can Lexus please confirm that the 12 volt battery does indeed charge when in EV Mode or when plugged into AC…