Single Pilot reported an NMAC event during final approach landing with a departing aircraft. The single pilot executed an evasive maneuver even though a collision was not imminent.

Narrative

I was returning to ZZZ from a VFR cross country flight from the south. I was utilizing flight following. It was a slightly busy time at ZZZ because many flights were departing. Upon entering the ZZZ class D I was instructed to enter a right base for Runway XX and report two miles out. I was level at 2000 feet MSL (traffic pattern altitude) on the downwind to Runway XX. Shortly before crossing the river I reported two miles out. A few seconds later another aircraft (type BE19) took off from Runway X. They turned out to the right at about 1700 ft MSL. Their ground track and my ground track were converging. They were climbing and I was level at 2000 feet MSL. I did not have this traffic in sight and I did not become alerted to them until I got the traffic alert on my Garmin avionics. Once I got the alert I tried to locate them; knowing that they would be at a similar altitude to me; crossing in front of me. Within a few seconds I saw the airplane cross directly in front of me; about 100 feet above and less than 1000 feet away laterally. I instinctively pushed the nose of the airplane down and turned slightly to the right to pass behind them. At about the same time I saw the airplane; I got a call from Tower letting me know about the traffic and telling me to pass behind them. I responded that I had the traffic in sight and I would pass behind them. I completed the rest of the flight without incident and landed on Runway XX.I don't think a mid-air collision was imminent in this case but I think we got a little too close for comfort. I think a few things could have been done differently to prevent this situation. It was a clear day so I could have done a better job scanning for traffic and listening to radio chatter to know other airplanes' locations and intentions. It also would have been helpful if Tower had alerted me of the traffic a little earlier so I had more time to look for them and react.The ZZZ class D airspace can be very busy during times of heavy flight training. My takeaway is that I have to be on high alert anytime I am in the airspace especially near the pattern. Traffic advisories from Tower are very helpful and very appreciated but I can't allow them to make me complacent. VFR collision avoidance is the responsibility of the pilots.