I can faithfully reproduce it.
I barely play any other games atm so it's just Overwatch for me. The odd thing is that it works perfectly in the preparation stage, before the fight starts. I can keep a continuous stream as mercy or fire the full clip as Orisa with no problems. But once the fighting starts the problems appear: Orisa's gun will start choking (same with D.Va) or Mercy's stream will get cut off even if a team mate is like 2m in front of me and is mainly standing still with a clear line of sight.
I tried some suggestions on the logitech support forums about disabling power saving on the USB port
I tried re-installing the game.
I upgraded to the latest version of logitech gaming software and will see how that works. I'll try with an older version as well and also your suggestion to turn it off completely.
I'll try a different USB port as well (although I think I tried that already)