Pilot reported a NMAC event during landing pattern training with a non-reporting Beech Baron. Pilot took evasive action to avoid a collision and was resequenced for another approach.

Narrative

At approximately XA:30; I was ending my 1 mile extended upwind and began my crosswind turn to enter right traffic as per ATC instruction. Right around this was happening; a Baron who had been coming in for a full stop (Aircraft Y) went around. He reported he was going to side step to the right; keep in mind traffic is going both left and right downwind. ATC directed the aircraft to continue flying west bound. As I am leveling off to enter the downwind; I get a 'traffic; traffic' alert on the TCAS and it shows him on a collision course at -100 feet below me. I immediately applied full power and did a left turn as he was coming from my 45 degree on the right. I climbed to approximately 1800 feet and was able to avoid the aircraft and got re-sequenced. After this happened; Tower made all traffic pattern aircraft full stop. Aircraft Z then asked on the ground why we full stopped and taxied back to [Runway] XX and Tower said it was because of the Baron that was just then landing. The whole incident is shown on flight radar at XE:27 UTC. The Baron was causing issues such as lack of communication and awareness before entering the Delta airspace