Pilot reported a NMAC event during landing low pass with a helicopter. Conflict dissipated before visual contact was established.

Narrative

On the first flight after engine maintenance at ZZZ; I was conducting a couple of low approaches over ZZZ before heading to my final destination at ZZZ1. During my second pass around the traffic pattern; tower cleared me for the low approach to Runway XX while I was in the left downwind. I executed a base turn and continued the turn for a short final and low pass. I slightly overshot final; putting me almost as far as taxiway. While descending through approximately 400 ft. just before the runway threshold (now lined up with XX); there was a helicopter approximately 50-100 ft. off of my right wing at my altitude. By the time I saw the helicopter; I could see there was no imminent collision; albeit it was quite close. I arrested my descent and turned slightly left. After I had already passed the position of the helicopter; tower called for me to side-step toward the river (left); so I further side-stepped; but the event was already over.I believe there were several factors that caused this near collision: There was a lot of radio traffic around the time of the event with a couple of helicopters in the airport area as well as several other aircraft coming and going. I believe the Tower Controller was possibly at the extreme of what he was capable of dealing with in terms of workload. I slightly overshot final (though this shouldn't have been a factor). My base/final were executed as a close approach as soon as I was cleared and possibly faster than what tower expected. My own situational awareness was overly focused on engine performance/instruments.Preventative measures I could do next time: Communicate clearly with tower if I plan to make a close approach during any maneuver. Do not over shoot final (even when there are no parallel runways; helicopters often use the taxiway). Do best to keep better situational awareness; though in this case; there was a lot happening in the pattern area and I did not expect the helicopter to be there based on the radio calls.