GA pilot reported they had to perform a go-around on short final when the Tower Controller cleared another aircraft to take-off without adequate separation.

Narrative

On an IFR flight and now in VMC I was cleared to land Runway XX -number 1- turning final the Tower cleared a Cessna 152 for takeoff. I was at ~300 ft. AGL and about 20 seconds from landing when the 152 was instructed to takeoff-no delay. I immediately leveled and told Tower I was on short final and now going to go around. Tower asked the 152 if he had crossed the line and tried to cancel the clearance. 152 had entered the runway. I again reported I was going around and was told to stay north of the runway. I turned right to the north and was next told to enter left traffic (which meant crossing the path of the climbing 152). I declined and said I was turning. Tower asked if I wanted to talk with ZZZ for another approach or cancel IFR and join the pattern. I said I wanted to land as ZZZ was my final destination. I was told to enter a right base Runway XX and cleared to land - number 1. While taxiing I heard the Tower say to another plane 'Aircraft Z - I forget - did I clear you to land?'I hope the Tower Controller took a break to get his head in the game. This could have been unfortunate. ZZZ is often a busy training airport. This morning it was relatively quiet with only two planes besides me in the area.