Not sure if this will help or not. but just like you it would shut my 4g off and reset it so I started to mess around with it and 1 way I was able to make it work was I made my phone into a mobile hotspot after that I had no trouble at all connecting. Not perfect or even how it should work, to begin with, but until they fix it at least you could do that to work around it. Hope this helps!
I too have had this issue. When I use a vpn on the phone, then connect to google remote desktop, I don't get the issue of the share screen cutting out after a few seconds of starting the session. I recently switched from the pixel 2 xl to the pixel 6 pro. I did not have this issue on the pixel 2 xl. That phone had a 4g branded sim card. The pixel 6 pro has a 5g branded sim card. If I had known before activating the new phone, I would have tested the old sim in the new phone to see if this makes a difference. If there is anyone with this opportunity, please test and let me know.
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