Cessna pilot reported not having separation from the proceeding aircraft while cleared to land and on short final; resulting in the pilot executing a go around and landing safely at the airport on the second approach.

Narrative

I was returning to ZZZ from ZZZ1 late on a clear day. The traffic pattern was busy. Tower told me to report three miles out and enter a left base for runway XX. I was cleared to land behind Aircraft Y which was on short final for a touch and go. Tower then asked if I could land behind Aircraft Y which was landing just over the threshold of XX while I was on short final. I accepted the landing clearance; believing Aircraft Y would proceed with the touch and go expeditiously. Aircraft Y made an extended roll on the runway before lifting off and I opted to go around; offsetting to the right while keeping Aircraft Y in sight as it made a left crosswind. Tower directed me to turn right for a right downwind to return to XX. The traffic pattern and tower frequency were both very busy. Tower directed me to squawk a new code and to proceed direct to a mid-field entry for a right downwind to XX but I was already in a right 360 to avoid potential conflict. At this point I believe both the controller and I had lost situational awareness in a busy traffic pattern. I advised that I was east of the field and northbound.I circled back to enter a right downwind and landed without incident on XX. The tower controller apologized for the confusion on the radio as I taxied to parking. I spoke to the CFI who was with a student in Aircraft Y and he said they kept the nose down before lifting off during their touch and go because he saw a target on TCAS very close above him. From his perspective that made sense; and my go-around would have been safe and routine in a quieter pattern.I believe this incident resulted from a combination of factors. The practice area is unique and ZZZ Tracon feeds IFR traffic into a high-volume VFR environment on busy VMC days. Tower frequency was saturated making it difficult for the tower controller to manage the traffic and for pilots to respond to directions. Changing the squawk code while circling back to wait for pattern re-entry made it difficult to maintain situational awareness. All this took place adjacent to ZZZ2 Class B; limiting options for spacing or delay vectors.