Flight Instructor reported an NMAC event while attempting to enter a crowed landing pattern.

Narrative

Haze with glare due to high pressure and setting sun. I was inbound ZZZ Runway XX from the east at a bearing of approximately 270 when setting sun made it difficult to see as I prepared to merge on the downwind. I glanced down at ADS-B to note 4 planes on downwind with a 5th to the south east of the field; unknown destination. I did not see planes on the upwind either visually or on ADSB. Poor horizontal visibility; blinding glare; good vertical visibility. I could not see the planes on downwind and was unclear about the plane to the SE intentions. This made making a tear drop or 360 to merge into the downwind a poor choice since I would again be blinded in the turn with known traffic in the area. The radio frequency was overloaded with many airports reporting on XXX.XX. I had announced inbound 15 and 5 miles and heard a plane was 10 miles west of the field with no stated intentions. Due to unknown status of planes but an ADSB visual on downwind; I announced and climbed 500 ft. above TPA to cross midfield; not realizing that I would be blinded by the setting sun. Airport borders on ZZZ1 Bravo to the north making crossing mid-field best option. I was blinded crossing midfield but maintained altitude and heading. Apparently another plane was also crossing midfield from the west but did not announce until he nearly missed me. He could see me as the sun was to his back; however; I was blinded and attempted to maintain altitude and heading. Between XA30 and XB41 there were 29 patterns flown inclusive of touch and goes to Runway XX at ZZZ. On review of flight aware tracks this included a possible training flight that made a 360 turn left flying upwind in downwind traffic to re-enter the downwind traffic east of the field. In addition; with numerous unclear; unnecessary calls on CTAF; it would not be possible to either make or understand radio calls to establish situational awareness of 11 planes making 30 landings either for final or touch and go. In retrospect after discussion with other pilots; the pilot who was with me; and including CFIs; a turn 180 to remove myself from the pattern was a possibility to reenter at a later time might have been the best options. Given that all flight schools in the area were very busy on the lovely day; it may not have been better at ZZZ2 or ZZZ3. Multiple touch and goes in busy landing traffic without consistent and accurate radio calls and an overloaded frequency were big contributing factors.