Air carrier Captain reported self-initiated go-around due to aircraft on the runway. ATC vectored the aircraft to another approach resulting with the aircraft landing safely at the airport.

Narrative

We flew the RNAV approach to [runway] XXL at ZZZ. We were cleared to land and told of departing (Company) aircraft ahead of us. (Company) departed when we were around 1;000ft AGL. It was then that we noticed a corporate jet taking the runway very slowly. We were not told about this aircraft; nor did we hear it get permission for line up and wait. We thought this was a runway incursion and expected to be told to go around. I told my FO (First Officer) this was not going to work and at around 500ft I initiated a go around. The corporate jet was still perpendicular to us and had not started his takeoff roll. At the time of our go around the corporate jet was cleared for takeoff; my FO then communicated our go around to the Tower. We were told to 'fly left of the runway'; not given a heading or altitude. I turned the aircraft about 30 degrees to left and initiated a climb. We had 2;600ft set in the altitude alerter so that was our intended altitude. My FO had the corporate jet in sight the entire time. We then received a traffic alert from what we think was another aircraft in the pattern. We were then given a heading of 140 and altitude of 3;000ft. We proceeded on those instructions and were given a downwind and landed uneventfully. We asked for a number for the Tower. I spoke with the Tower Manager; and he said the Controller 'Had a lot of things going on' and assured me that we were not at fault. I filed this report on a general Safety concern for ZZZ. I don't believe we had a near miss with either aircraft; but this was definitely a messed up situation.Suggestions: I don't know if there was training going on in the Tower; but they definitely were trying to accomplish too much in the time given. My FO was performed very; very well in this situation and the communication between us is what I believe mitigated a huge amount of risk in this event.