SOC dropped, battery status to one bar / pip

Today I went to the national car test (passed. but), when the car has been returned to me by the employee of national car test center I noticed one bar on the SOC. This happened for the first time.

Additional notes:

1) recently (about 4 weeks ago) I had to temporarily replace for second hand (20 bucks) 12v small auxiliary battery (long story as to why I had to do it)
2) recently (withing last four weeks) I noticed high temperature in the boot compartment, I tried to investigate and the ducting leading from the HV battery was really hot, which means that my battery was really hot too.
I tried to explain this to myself that this might be due to HV operating at higher levels due to unknown state of the replaced 12v small aux battery (second hand product)

3) Today I noticed that technician at the test center used some spring assisted bar to press the brake on the car while he tested the car, I recon that maybe he have had powered off the car while doing so, is it possible that this might have contributed to the dropped SOC ?- it's just my guess.
Anyway I'm starting to worry a bit.

I'm thinking to replace 12v aux battery to brand new battery and then test the operation of the fan and whether the temperature still rise. - is it good idea?

Or should I just seek for the testing tool to determine the status of each of the modules?

If so, which testing device can handle this task? I heard from this forum about ELM obd bluetooth adapter. I use android device, would this be okay or should I look for another device perhaps scangauge?

Could any of those with knowledge provide me with advice and possible precautions I should take?

Any help appreciated.