Air carrier Captain reported at destination deplaning the flight crew had to assist a stranded wheelchair passenger to enter terminal area. Once inside the terminal the Captain realize they had transported an undocumented battery powered mobility device.

Narrative

While parked at the gate and just as we were finishing boarding; I needed to speak with operations on the nature of our delay and to communicate our wheels up time for departure. I was unable to contact operations via radio or phone. This particular gate / parking stand utilizes airstairs or a boarding ramp and is a long walk from plane side to the terminal making it difficult to leave the aircraft to speak with anyone in operations. I advised the CSR (Customer Service Representative) at closing that we had been unable to contact ops and was told that was normal because often times nobody is in the office with the radio or phone. I believe it is important to be able to communicate with someone in operations while on the ground for a range of time critical reasons including a medical; aircraft; or customer service issue.Gate / stand19 (and gates 17-20) utilize ramp access and airstairs or a boarding ramp to the aircraft. Cones are used to mark passenger paths to each aircraft parking stand. As we began boarding the ramp cones were not set to close off access to stand 20 (which was to our left) for passengers to easily identify the path to our aircraft at stand 19. Initially; there was also no airport personnel present to guide passengers to the correct path to access our parking stand. As passengers walked out of the terminal; they unknowingly walked straight ahead (instead of turning left) to parking stand 20 and then began walking across the ramp towards our stand outside of the designated pathway. Ramp personnel saw this and guided passengers to the correct pathway to access the aircraft. Additional cones were put in place and a CSR then came out to guide passengers to the correct path. I have attached a picture showing the lack of cones blocking the path to stand 20 and then across the ramp to our parking location before cones were put in place. There was also a 737 parked at stand 17 boarding simultaneous to our aircraft. The pathways for our gate and gate 17 were side by side with a combination of cones with yellow and black caution rope tied between and cones with nothing between. Several passengers switched to the wrong pathway when they encountered cones with nothing in between and had to be corrected by the CSR monitoring the boarding process. The CSR was also having to direct passengers where to place gate checked baggage and would be distracted from monitoring the pathways leading to the potential for a passenger to board the wrong aircraft. When the CSR was correcting passengers on the wrong pathway then we had customers unsure and confused on where to drop their gate checked bags. The entire area is very confusing with multiple pathways designated by cones to at least four different parking stands and no signs indicating where to leave gate check bags. There is an elevated threat that passengers board the wrong aircraft; inadvertently walk out of their walkway and into an area with aircraft movement and ground service equipment operations; or leave their gate checked bags at the wrong parking stand or in the wrong location by the aircraft.About ten minutes after deplaning on arrival; I walked down the boarding ramp to access the terminal. I noticed a passenger in an electric wheelchair with her travel companion alone just in front of the nose of the aircraft out of view from the flight deck. This particular passenger had needed an aisle chair for egress from the aircraft and had been assisted down the boarding ramp to her electric wheelchair. Unfortunately; after getting in her electric wheelchair; it did not work as the battery was not connected properly and since personnel who had helped her in the aisle chair did not wait to see if she was able to get to the terminal; they were stranded needing assistance on the ramp. I was able to assist in helping the customer stand while her travel companion reconnected the battery and they were on their way. I was disappointed to see this customer and her travel companion by themselves needing assistance with nobody in view to get help. This also made me realize we had likely carried an electric battery operated wheel chair and had not been given the device tag during boarding in ZZZ.