Captain reported loss of surface movement control and damage to a Nose Wheel Assembly during push back without the tow bar connected properly. The flight was cancelled and the aircraft was turned over to maintenance for action.

Narrative

At approximately XA:20PM L; we began push back process with ramp at ZZZ. We had not completed the below the line checklist as we were still waiting for performance numbers but were otherwise ready; so I elected to at least get the aircraft hooked up to the tug and the parking brake released to limit timeline lateness.I informed the Ramp that we had nose wheel steering disconnected and parking brake set. Ready for brake release. They responded with approximately; chocks removed and ready for brake release. I released brakes and felt a normal small aircraft movement as the brake was released and the weight of the aircraft is then managed by the tug linkage. At this point ramp indicated that the chocks were still in. I asked why they had reported chocks were removed; and that this can cause the chocks to get stuck under the wheels. The Ramp person said something approximating that she had misspoke and that chocks were in fact clear. I advised Ramp then that we still had one checklist left to run and to standby for instructions and that we would be ready shortly. We then got performance numbers and completed the below the line checklist.I then called Ramp and verified they were still ready for push and that we were calling Ground.We were parked at Spot XX; and ZZZ Ground asked us to push into the alley after another aircraft had cleared. This would be a push of ~300 ft. and ~120 ft. to the right from the tugs perspective.I relayed instructions and they read-back correctly and we began push at approximately XA:25PM L.We pushed approximately 40 ft. and only just started to get pushed to aircraft left by the tug moving slightly to its Right; and I noted normal mechanical clunks and bumps; which are common through the hard linkage with a tow bar that are from the metal slipping at the tug end being transmitted through the tow bar to the NLG. Push back seemed normal otherwise.Tug advised cleared for engine start and I directed FO (First Officer) to set flaps 2; start Engines 1 & 2.Shortly after; the tug reduced their throttle to slow down the push slightly; and then I heard a louder 'clunk' and short grinding sound; and noted that the tug was no longer moving at the same rate as we were and recognized that we had become disconnected. The Tug Driver got a whoa whoa! Set brake! through before the slack in the intercom line ran out and got yanked out of the jack. The Tug was approximately 20 degrees to aircraft left and we were traveling ~5-8 MPH and were just starting to slow down at time of disconnect. (I think the slowing down and the transition to the aircraft inertia pulling the tug and tow bar is what pulled the tow bar off the NLG.)At approximately the same time; I told the FO abort start. We're disconnected.The [report] about the aircraft in ZZZ1 from the last 2 months came to mind immediately regarding the dangers of slamming on the brakes if rolling backwards; so I applied foot pedal braking just enough to where I could feel them engaging and accepted a gentle rolling stop. We rolled about another 40 ft. before coming to a stop. I then applied the emergency brake and starting taking stock of the situation. Total distance pushed + rolled was ~100 ft. FO later reported we only got to about 20% N1 before I instructed him to abort start when we debriefed with the Company Line Maintenance Supervisor at ZZZ afterwards. Engine 2 was never started.After the FO reported safe aborted start; we had to wave to get the left wing walkers attention and I gave him the cut throat signal to indicate that we had stopped the start. This got the tow team focused back in towards the plane and then they saw that the tug was no longer connected.We contacted ZZZ Ground and told them that we had become disconnected during tow. They reported we were not blocking the alley and take as long as we needed to safely return to gate.We then contacted ZZZ Operations informing them of what happened. I then made a brief PA to the Passengersstating that we had an issue with the tow bar during the push back and that out of an abundance of caution; we would be returning to the gate to ensure that there was no damage before continuing with the flight.I then opened the Captain's window to communicate with the tow team; and additional staff that had arrived after the incident became noticed by the rest of the Company ground support staff at ZZZ. I asked the FO to monitor the radios while I worked out a plan with the tow team to get the aircraft back to the gate.When they started bringing the same tow bar from the incident; I asked the lead; to try using a different tow bar in case the old one was defective. They got a new tow bar; tug; and tug driver and hooked up. The lead reported that he could see damage to the inside lip of the rim of one of the NLG wheels when they attached the new tow bar. Because of the damage to the tug headset; we used hand signals to get back into the gate.After we got back to the gate; I called Maintenance Control and we coordinated getting the Ramp brought back to the aircraft. Maintenance Control reported that there were no Maintenance immediately available on site and that I would need to go document the damage and text it to them. I then made a PA on my way out at the FWD FA station; reiterating that we had an issue with the tow bar on push back and that as soon as I had more information about what we needed to do to continue safely; I would report back to the passengers.I got off the aircraft and photographed the damage to the NLG RH WHEEL ASSY inner rim/lip where weights are usually mounted for balancing. When the tow bar disconnected; it gouged about 2-3mm of metal off of the lip along 40% of the radius of the Wheel Assy; with up to 5mm in some places. Large metal shavings were also present laying on the lower inner face of the Wheel Assy as well. After texting photos to Maintenance Control; they reported that this would ground the aircraft. I returned to the FWD FA (Flight Attendant) station quickly briefed the FO and FWD FA; then made a PA informing the Passenger that there had been damage; and that the aircraft was unfortunately grounded. We would be disembarking the aircraft shortly and everyone would need to go inside and check in with the Gate Agent on whether we would be getting them on another flight tonight; or tomorrow.While the passengers disembarked; I called Dispatch; entered the damage into the Maintenance logbook per Maintenance Control's instructions; while the FO coordinated hotels and transportation for the crew. The on call Maintenance then arrived before we departed; and I quickly debriefed him on what had happened. The ZZZ Line Maintenance Supervisor also arrived before we left; and we debriefed her as well.Due to how exhausted I was after getting to the hotel; I recorded some notes and elected to call Operations the next day. Operations texted me the next morning before I got chance to call him; and I gave him a short debrief then.Paint/color/flag tow bar connector apparatus to clearly delineate when it is open and unsafe; and closed/safe.Currently there are just two different holes with a locking peg that in dark/night conditions; you cannot verify but from somewhat close range (less than 10 ft.); that it is fully back and locked in place in the correct position; especially if the peg is in the wrong hole.