Thanks for the tip! I have installed the newest firmware - SurfacePro7_Win10_18362_20.122.27379.0 - and the TypeCover started to work! It is already several days without any problems. The keyboard works all the time in any tilt position.
Hopefully, Microsoft spotted this extremely annoying problem!The keyboard stopped working completely. I retract my previous good words towards Microsoft.
In two months I am changing SP7 for ThinkPad X1 Yoga 6gen. Never going to get back to Surface.
Yeah, it's still flaky, although much better than before, so I still hope that MS will completely fix it.