Check in your BIOS settings... I'm betting the screen turning off when on-battery is hardware-driven from a BIOS setting.
While you're in there, check to see if there's a built-in utility to update the BIOS / UEFI, and check to see if there's an update. If there's no built-in utility to check for updates, check the Dell support website for a firmware update.
If there is an update available, it's most likely in a Windows-only file format... in that case:
My computer is an HP, but the procedure will work for any computer.