GA student pilot with instructor reported an NMAC while on the downwind leg to PLU non-towered airport.

Narrative

My CFII and I were working on touch and goes at PLU. This was my first time to this airport and my CFII wanted me to become familiar with airport and the local procedures.During the 2nd time around the pattern is when the incident occurred.I made a radio call on CTAF to advise I was turning onto the downwind leg for Runway 35. I made the turn and continued on downwind leg. Prior to getting abeam Runway 17; Aircraft Y descended into view on the 45 degree to TPA and turned to align with the downwind for Runway 35. Aircraft Y failed to observe the traffic pattern and yield to established traffic when entering on the 45. At this point I turned to the right to avoid the aircraft and continued to do a 360 degree turn to and re-enter the downwind. We announced on CTAF what had happened and our current intentions. Aircraft Y acknowledged our presence after we called out that they had descended on top of us by responding on the radio to us with the comment 'No Bueno'.The radio calls from the Aircraft Y were all without registration number.I was not able to determine the tail number of the other aircraft due to the 360 and the lack of ADS-B data.We also did not see the aircraft on Foreflight paired with the Sentry portable ADS-B receiver; so they must not have been transmitting any ADS-B data. PLU is inside the '30 NM Mode C & ADS-B OUT' vail of SEA. This would have increased the situational awareness and alerted us of the nearness of the aircraft and actions could have been taken prior to the incident.In reviewing my track log; I did notice that I was about 100 feet low. I had set the altimeter to the correct setting from the local AWOS-3. In any case; there were only two settings during the flight. ZZZ1 was 29.84 and PLU was either the same or 29.81. I'm not sure if 29.81 was for PLU or when returning to ZZZ1.