Pilot reported communication issues with the ground crew on pushback.

Narrative

Standard three-man push. Beginning of pushback was abrupt and not smooth at all; but not bad enough to be considered unusual just rough and unpleasant. Aircraft was pushed back; turned 90 degrees from J-line; and placed approximately on taxiway/lane centerline. 'Brakes Set' communication from pushback was garbled and hard to understand. I set the parking brake at the end of the push; while the FO (First Officer) started engine #1 followed by two. 'Towbar disconnect / bypass communication' was also garnered and hard to understand. I cleared off the Ground Crew. I counted three people; tug; tow bar; pin; and COMM bag. I turned my attention back inside the aircraft to complete before taxi procedures. I noticed the tug had not driven back to the Safety Zone and one Ramp Agent approach the nose of the aircraft.He made a motion with his hands; which I could not decipher. We heard him messing with the Ground power/Ground COMM door for approximately 30 seconds. We did not receive any verbal communication; as both of us were monitoring the flight service inter phone. The Ramp Agent then reappeared on the Captain-side for the aircraft; waved bye and proceeded back to the gate area with the Tug Driver and tug. We had zero indication the pin had broken and assumed they were being cautious and double-checking that the Ground COMM door was secured for flight. We departed for ZZZ1 and arrived without incident. Upon arrival at ZZZ1 Operations Agent informed us that ground operations reported the tow bar shear pin broke during push. We then wrote up the event in the aircraft logbook. Contract Maintenance then inspected the aircraft and did not find any damage.