Customer support is denying service

I have a loq i5 12450h rtx 3050 6 gb bought in November, 2023 along with a 3 year premium care.

My laptop shuts off immediately after the charger's disconnected, no warning, it just dies. The battery in windows indicates either 0% or 100% charging, even though battery capacity shows 97% and health is in good condition. After this power loss, the laptop takes ~10 mins to boot and performs very poorly. So, I have to use charger at all times.

I contacted lenovo and, the technician changed the motherboard but as the issue still remained, he again replaced it with my original motherboard and, told me it's battery issue and, the battery is out of warranty so, I have to purchase it, as my premium care plan doesn't cover the battery.

My confusion is the battery cells aren't worn out as it says 97% capacity and good condition. The laptop instantly dies when unplugged, which probably suggests battery BMS failure, not normal wear? A worn battery would still power the laptop for at least a few seconds if not minutes but, mine doesn't even do 1 second. I think this is because of the battery's internal hardware and that should be covered in the warranty, as it's not battery wear.

So, can anyone please tell me whether or not I could convince lenovo support that it's hardware defect and not battery issue, as the report shows battery is perfectly fine? Any advice for the battery replacement?

Thank you.