False low battery warning then hibernation

Run a battery report (open a command prompt with admin privileges at type powercfg /batteryreport). What are the current and design capacities of the battery in the report?

That model came out 2 years ago. Try replacing the battery with a genuine new one from Dell if available. Today's batteries fail much quicker now. 18 months to 2 years of life is common now. The battery meter is not always correct especially if you always keep the adapter plugged in--which makes the battery fail quicker.

Design = 49,985
Current = 48,982

That should be validation that the battery is OK. If you haven't done so,
1. Power off, unplug the system.
2. Remove the base cover and disconnect the battery from the system board.
3. Hold the power button for 30 sec.
4. Reconnect the battery and power on to a setup screen (F2 at powerup). If the system continues to run without issue on battery, then,
5. Boot into Windows and see if that solved the problem. If you still see the power-cut error, it could be a faulty power management driver -- try reinstalling those (or better, a factory reset of the OS).
If the problem continues, it's either a battery issue or a mainboard issue -- the battery is $150 or less while the mainboard will be pushing $1,000 -- if you have to start swapping parts, the battery is the place to start.

Service manual

https://www.dell.com/support/home/en-us/product-support/product/xps-13-7390-2-in-1-laptop/docs