SR20 Pilot reported while in the pattern encountering another aircraft that was not transmitting on the CTAF; and was in direct conflict with his aircraft resulting in the pilot taking evasive action to avoid a collision with the other aircraft.

Narrative

On the upwind leg departing ZZZ Runway XX on a SOLO flight and in a crowded pattern; I extended for an incoming Aircraft Z on the 45 for left downwind runway XX. Still in the climb to 2000 ft I noticed a Cessna 172 around 3-4 nm in the south east (on my 10/11 clock); at around 2700 ft. I assumed they were transitioning east to west since they were far above TPA and also didn't do any calls on the ZZZ CTAF. As I already had reached 2000 ft and still being on the extended upwind leg; I noticed that the Cessna was descending. I monitored their altitude and soon they were descending on collision course nearing less than 500 ft separation. To evade the conflict I started a right crosswind turn while making sure there was enough separation to the entering traffic I was extending for. I didn't evade to the left to avoid a turning-into-each-other situation when the Cessna would alter their path to the right for traffic avoidance as soon as they would see me. Also I still was not sure what the desired flight path of the Cessna was; but I didn't suspect a direct downwind entry for right downwind XX coming from the south east far above TPA. While in the turn to right crosswind I noticed that the Cessna was still on collision course; so I turned directly into downwind to get myself on an evading flight path. As I was on downwind the Cessna followed me closely while still descending from around 2300 ft. I couldn't believe that the Cessna was still descending while in this close proximity to another aircraft in the pattern and while not making a single call on CTAF nor answering to my calls of intention. The situation was too dynamic for me to call them out by their callsign on frequency; but I had made calls for extending for a certain Aircraft Z callsign (with answer from that Aircraft Z) and have also made callouts for crosswind and downwind turns. As we were in close proximity in downwind and after I had lost visual contact to the Cessna due to me flying in front of them in the downwind the ADS-B indication of them showed them directly on top of myself while they were still descending. I intuitively lost around 100 ft for separation but was really in shock how they could still not see an aircraft that close to them and below; considering a C172 is a high-wing aircraft. To get out of the situation I set full power and out flew the Cessna; while making another call. I left the traffic pattern as soon as I was clear of conflicts. As far as I can recall the ADS-B altitude indication showed them only 100 ft above me at the closest point.As soon as I got back; I checked the whole situation on flight radar. It looks like there was always some horizontal distance between them; but this flight leaves me really concerned about traffic pattern procedures for ZZZ. Flight radar shows them entering the left downwind runway XX via a direct downwind entry coming from the south east in a continuous descent from over 3000 ft. This was one of the main reasons why it took me considerably long to identify them as a traffic pattern conflict and not a transitioning conflict. Also; clear intentions of the Cessna on CTAF would have led me to avoid them to the left early or to just extend upwind until they are clear. For myself I reflected how strong a bias/assumption of the intention of another aircraft can be; since it really shocked me; that they never stopped their descent and in fact performed a direct downwind entry at an uncontrolled airport with a packed traffic pattern (6+ a/c; some on entry). Since this aircraft landed in city X right after me; I can confirm; that there were no issues with the radios of that particular aircraft. Suggestions: Contact aircraft owner/flight school; make sure awareness for procedures at uncontrolled airports and importance of CTAF callsStrictly prohibit 'cowboy' flying on uncontrolled airports.