A320 pilot reported engine failure ECAM message and returned to departure airport.

Narrative

Flight started with a normal preflight; pushback; taxi out; and take-off. I was the Flying Pilot of this flight. Climbing through FL210 with autopilot and autothrust on; we experienced a ENG 2 Compressor Vane ECAM. I monitored the aircraft and took ATC communications while the First Officer accomplished the ECAM. I leveled off at FL230 while notifying ATC that we were have an engine issue. We did not [request priority handling] at that point in time. Shortly after this ECAM while the First Officer was going through the ENG2 Compressor Vane ECAM; we received an ENG 2 FAIL ECAM. I subsequently [requested priority handling] with ZZZ Center; and told them we needed to return to ZZZ. They responded quickly and gave us a turn back to ZZZ while we maintained FL230. The First Officer and I worked through the ECAMS and checklists associated with the above. As we were completing our checklists; the First Officer called the flight attendants to suspend the cabin service and advise them we were going back to ZZZ. I worked with ATC to give them information they asked for; souls on board; fuel quantity; etc as we progressed back to land. I briefed the flight attendants; told them that no prep of the cabin was needed; and that we should be on the ground in about 20 minutes. I made a PA announcement to the passengers and told them what had happened; what to expect; and that we were returning to ZZZ. ZZZ Approach set us up for a visual landing with ILS backup on [Runway] XX. A successful single engine approach and landing was accomplished. Fire/Rescue equipment followed us upon landing and inspected the aircraft after we cleared the runway. (We were approximately 6000 to 7000 lbs over max landing weight and the temperature was in the mid 90's so I requested they inspect our wheels as the brakes were quite warm.)We were subsequently cleared to taxi to gate with firetrucks in tow. ZZZ Operations gave us our gate assignment and we taxied to complete the flight. After the aircraft was secured at the gate and parking checklist was completed; the First Officer and I took a couple minutes to debrief ourselves before opening the cockpit door. I then went into the cabin to make an announcement to our passengers about what to expect. I was able to coordinate with the gate agents and operations and we then deplaned; the passengers to re-accommodate them. I then debriefed the flight attendants to check on them. After a short time; Company Maintenance arrived at the aircraft. Of note was one of the mechanics that came onboard and made a comment that we really didn't have any engine problem or damage and that We've seen this kind of thing before." I thought that to be kind of an odd statement with the ECAM screen still showing ENG 2 FAIL.I can't speak for the First Officer; but I felt like he just blew off what had just happened with our aircraft. Enough said about that."