welcome back !
The trouble is that in trying to focus on essentials the arguments become diffuse. Hence the supersonic intake producing thrust argument. If the engine can hold the shock at an advantageous position in the inlet then yes the net force obtained by integrating the pressures over the inlet can be a positive thrust but not without the engine ! The thrust is not an intrinsic characteristic of the inlet nor of the nozzle and I think that's the source of confusion.