 Turned out to be faulty BIOS chip. Needed a chip swap.
(This story begins here but once I tracked down what exactly causes this issue, I decided it's easier to write a new post than rewriting the original one) In short, my XPS operates properly only if the Service Tag is NOT SET. If I set it, it starts to crash when and only when running off an AC adapter. Out of warranty September 2019. A week ago, I got the following warning on boot: "The Service Tag has not been programmed. This system will not function properly without a Service Tag". I don't remember installing any updates, and no new hardware or BIOS updates or configuration changes. I ignored this warning for a few days. Its important to state the system operated normally during this period. Once I finally went into BIOS and set the service tag (and double checked it), the system started to malfunction: What I tried & details   What finally worked: BIOS Recovery and NOT setting the Service TagAfter a crash I tried to turn on my laptop while it was still plugged in. On boot it displayed a BIOS Recovery prompt (it didn't show one before). I went with the first option ("Repairing BIOS", I guess), it performed the recovery, rebooted and voila — my XPS runs off an AC adapter again! Did a number of tests (stress test, video rendering) — it doesn't crash now. I guess the same prompt can be triggered using this guide. After a few reboots I started again getting the warning "The Service Tag has not been programmed. This system will not function properly without a Service Tag". Since all of my issues began once I set the service tag, I ignore this message for now and just hit "Continue". As I mentioned, the system works absolutely fine now, aside from the service tag warning. Since I couldn't find anything like this issue documented, I would like to know how to fix this issue "properly".
XPS 15 9570, setting Service Tag, crash while operating off AC adapter