I have had an identical problem a few years back, with a Samsung 2 in 1 that worked perfectly on AC, but had exact issues on battery.
It was the "power saving" capability of the GPU that triggered it on battery. So simply disabling this is the integrated Intel GPU control panel (in Windows) fixed the problem. Laptop is still running now and works with my sister in law.
I have had an identical problem a few years back, with a Samsung 2 in 1 that worked perfectly on AC, but had exact issues on battery.
It was the "power saving" capability of the GPU that triggered it on battery. So simply disabling this is the integrated Intel GPU control panel (in Windows) fixed the problem. Laptop is still running now and works with my sister in law.