If you want to know the status of your main battery then it needs to be load tested while disconnected from the Aux battery. I'd consider having both batteries independently load tested if you want to run with both batteries.
As mentioned, if one battery is shot you need to either replace both or bypass the Aux battery, turn off ESS by pressing the button or buying tech to do it for you, and just replace the main battery. Information on how to do this is available on request.
As a warrantied repair though, the dealer will likely be unwilling to bypass the Aux battery.
If I follow you correctly the reason you are opting for keeping the factory dual battery system is for not (so much?) running ESS events, but as an earlier warning system of sorts for detecting battery failure: a particularly critical issue for you given your off roading interests and the isolation from vehicle service such pursuits can create.
The problem I respectfully see with this approach, and maybe I am missing something, is its tendency to create a “self realized prophesy” of sorts if you will, in other words increasing the chances of the very battery stranded state you seek to avoid, by continuing to allow the smaller of the two batteries, with a MTBF (mean time between failure, i.e when it “craps out”) that I strongly suspect is far lower than, on average, of the main battery. And of course given their parallel connection that small battery's demise can negative effect the main battery (or vice versa.)
As long as you are not running ESS events, off roader or not, is seems to me that bypassing the Aux battery is the way to go. If your a mall crawler, acquire a portable jump starter. And if you're an off roader like yourself, might you consider a Genesis Offroad solution: which in fairness can be a costly endeavor?
Disclosure: I run both batteries factory, ESS events, and I trickle charge.
I'd also think that load testing the main battery, operating alone, before such off road adventures might be a better, or at least another way to detect and address battery problems beforehand.
The vehicle's built in tests you describe are ones for voltage alone and suffer from all the limitations such tests have at detecting a battery's ability to do its true job: deliver and accept charge, as a load tester reveals.
