XPS 9560 switches off abruptly when on battery power

I have tried to fix my new/refurbed XPS 9560, didnt work, need help.
I started using it properly yesterday, and it switches off abruptly (as if someone would have pulled the plug from a desktop) randomly when on battery power. Battery indicator at that moment can show anything from 60 to 98%. It refuses to start again while on battery, but if I plug the electricity cable in then i can start it. It has not switched off with AC adapter plugged in.
The fans werent sounding much before switching off, and I generally doubt it is overheating.
I ran the Diagnostics from BIOS (by pressing F12), no issues, all passed well. Battery health 96%, battery manufacturing date 6/4/2021. I also ran battery check from cmd. It returned design capacity 96,991 mWh, full charge capacity 94,073 mWh. With other words from these tests battery looks ok. No issues in Device Manager.
I do notice that if i simply browse it doesnt switch off (yet) - but i dont need a laptop for browsing. Two of the switch-off events happened when i was in my video editor (DaVinci 15), exporting a vid. I googled this, and folks write it could be CPU or MB overheating, - but then for me it does NOT happen if i am on AC power, and therefore it doesnt look like overheating.
I tried to check the reliability report. Now, I dont know what most of it means, anyways when DaVinci (video editor) stopped working, every time the problem event name was BEX64, and fault module ntdll.dll

I tried to reset BIOS to default, problem remained. Dell's SupportAssist refuses to start on my laptop so I mostly use Dell Update to find drivers etc.
I also have encountered two BSOD in last two days, - before I discovered the laptop switches off randomly/when working harder? - the first being CRITICAL_PROCESS_DIED (mostly hardware malfunction or driver issue; if i read reliability report correctly, live kernel event 1cc) and the second UNEXPECTED_STORE_EXCEPTION (mostly driver issue; possibly live kernel event 144).
I am also thinking if it could be something with the software. I could reinstall Windows if that could help

I could send the laptop back where I bought it, but I really need it for work. Im already behind. To add insult to injury it is nearly impossible for me to find a laptop that has specs I need here in Sweden so if I send this one back i dont know if I find anything I can use. Would it be completely stupid to keep this laptop and use AC power when doing critical work?
All advice is much much welcome, and maybe there's someone smart who can put 1+1 together and see what my data means and what can be done..

 

Some info came up that raised a crucial question.

What happens is if I render the vid at 10fps, I can. If I render the vid on max speed, the laptop switches off. Once I understood the issue is with DaVinci video editor I went into DaVinci forums. This rendering issue (max vs 10fps) is known and indicates too low capacity. In this case, low battery capacity, because on AC power there is no problem.

Furthermore, this is what I got from guys on DaVinci forum: "In my experience, the only laptops that work well with DR under battery are recent MacBooks. Older MacBooks and all Windows laptops should be on AC power when rendering" and "we had to replace a 2000-watt UPS with our big Mac Pro on some difficult jobs. Now, we have a 3000-watt model and the problems disappeared"

So I guess the crucial question I want to ask, is - can a healthy but weak battery react to too high demands in a manner that it abruptly switches down the laptop (as if a plug would be pulled and you lose all your progress ofc) and refuses to start unless I connect it to AC adapter?
If yes, I have my answer. If no, then the battery gotta be faulty and might cause damage to the laptop, I might need to look for another battery or laptop if the vendor doesnt cooperate

 

I might have found the problem and the solution!
A bit incredible but.. THE POWER PLAN. In the power plan the cooling fans were inactive in battery mode (advanced power settings - processor power management - system cooling policy(battery) - it was set to Passive and I changed it to Active now). The laptop switched off in a typical overheating fashion with no warning when CPU was on high load and heating up, but the CPU cooling was inactive and on passive mode when running on battery!! It was CPU overheating!
I did a short export already with the cooling on (in active mode), on battery power, and the laptop didn't switch off! I will still test but I think this was the problem!

 

Did the power plan turn out to be the issue? Hopefully it was, this would have been an easy fix that way

 

Power plan, but also overheating. There is a possibility that overheating had damaged the battery. The vendor sent me a new battery which i have changed now. I also turned off intel turbo boost in BIOS. And am looking at even further possibilities to cool down the laptop such as undervolting, and maybe changing the thermal paste inside as Dell's original is thought to be not that good.
Thing is that the laptop had an insane overheating problem when i got it. I measured inside temperature and when i just was IN the video editor it reached 99 Celsius (with passive cooling in heating plan, with intel turbo boost on and old battery). Thats insane.

 

Oh nice, its good the overheating has damaged the battery though and not something harder or impossible to replace. Undervolting should help with temps yeah but I don't know if that's possible on a CPU that is not overclock-able, if it does need to be an overclock ready chip on Intel the name ends with a K, so "3900k" as an example, and apologies if you already know this.
Have you got a paste in mind? Thermal Grizzly is regarded to be very good, I personally use Noctua in my laptops and my desktop which is a full on gaming PC and that thing (Ryzen 5 5600X) hasn't yet gone above 70c even pushing intensive games and programs. Might be worth staying away from liquid metal, not heard too many good things about that stuff.

99c simply in a video editor is insane, hate to think what damage that could do should you start editing some big project. Hopefully now its sorted too, glad you found the issue & got a new battery sent