A C152 pilot in the Tower downwind pattern reported a NMAC when a departing aircraft turned early into their course.

Narrative

I was doing night pattern work at ZZZ; doing touch and go's on Runway XX; along with other traffic. Traffic ahead of me; Aircraft Y; is told by Tower to make right traffic after their touch and go. I land and am told to extend; make left traffic and do so. As I am flying the left downwind; Tower clears Aircraft Y; number 2 to follow traffic on final. Aircraft Y reads back call with traffic in sight and proceeds on the right downwind. Aircraft Y descends early however and they make their right base turn too soon; cutting off the inbound traffic on final. Tower nearly immediately alerts them of this and tells Aircraft Y to go around; fly runway heading. Aircraft Y responds; confirming a go around. Tower then tells them to continue flying runway heading; and that they will then turn to enter the left downwind. Aircraft Y reads back that they will proceed to left downwind. I am watching this happen and see Aircraft Y change course during their climb out from what looks like runway heading to directly towards my aircraft in the left downwind at pattern altitude. I don't think he sees me during this as he is in a steep climb. He proceeds in his climb and then Tower alerts him to his course and that there is traffic ahead. Aircraft Y does not adjust his course and I have to immediately dive to avoid a collision; dropping around 150 feet as he flies directly overhead; about 60 to 100 above my aircraft when directly overhead. After a few seconds Aircraft Y then requests to leave the airspace and depart to the east. Tower gives him a course to follow before being allowed to depart. I believe both the pilot of Aircraft Y and Tower are at fault to differing degrees. The pilot is at fault on two counts as they did not keep track of traffic ahead of them and entered their base turn way too early; forcing the go around in the first place. They are also at fault of not heeding the direction of Tower to follow runway heading before entering the left downwind; instead heading directly towards the midfield left downwind. Tower however also should not have made two course directions at the same time. By telling the pilot to both fly runway heading and then that they are to enter the left downwind; the pilot of Aircraft Y was much more likely to miss identify where they were supposed to head. To prevent this from happening again; the pilot of Aircraft Y needs to keep track of traffic ahead of them in the sequence; and Tower should space out when they make course guidance into separate calls for different courses.