Surface abruptly shuts down when screen off or sleep  

Windows iso can be used to test drive various Windows versions and builds.

Microsoft Windows and Office ISO Download Tool

The most recent Win is 22H2 on Sept 22 (this could be good to test... Even if the actual Win is the same 22H2, but probably a different build ?), otherwise you find 21H2 from Nov 2021.
Could I download this 22H2 ISO and make an in-place repair, building the ISO from C: ?
But then I should block Win updates for a certain period, to check how it behaves with the shutdown...

If you want to test different Windows versions / builds then use backup images.

Multiple backup images can be saved and restored as needed.

Windows 10 1607 could be tested, etc.

Just to try and tie some ends together, I haven't personally done anything of use to fix this issue but my reddit thread got following reply which might be of interest:

I have the same issue. it's a software issue since fresh installing Windows without the surface Firmware gets everything repaired. Once you install the latest Firmware updates, you're doomed.

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All the credit to u/RAZ70R over at reddit, here's a workaround that seems to have done the trick for me without the side effects the power workaround has:

No need for anything else. just do the following:

Device Manager - System Device - intel management engine interface - Power management - (uncheck) allow the computer to to turn off this device.