A Tower Local Controller reported they cleared an aircraft for takeoff in front of another aircraft on short final. The landing aircraft initiated a go-around.

Narrative

I am a newly certified CPC and this was my first shift of the day. I was on the Local Control position with my supervisor behind me working standalone Controller in Charge (CIC). Aircraft X in the left pattern for Runway XXL had been given a downwind extension to allow spacing for a departure off the runway. After there was enough space; I allowed them to turn base and cleared them for the option. At the same time a few departures and arrivals were also taking place on the parallel runway (Runway XXR); and another aircraft on the ground had called up on my frequency to notify someone pulling up to the runway that their baggage door was open. I stepped in to facilitate the discussion and ensure that the aircraft did not need to get onto the runway while maneuvering to conduct his check of the door. Another aircraft was then short-final for Runway XXR as well.After this was adequately resolved on Runway XXR; an Aircraft Y called up for a departure off XXL at the Taxiway X intersection. The Ground Control position had previously informed me that they were a departure along the Shoreline toward ZZZ1's southern airspace; so I called over the shout line to coordinate per the LOA. The Local 1 Controller was having problems understanding the coordination; so it took a few back-and-forths to clear it up. In the meantime; Aircraft X had been making a 1 mile base turn and final; and in his descent toward the runway had now dropped off the radar. Once ZZZ's Local 1 Controller finally approved the transition; I made a quick glance up at the radar and out the window; but missed seeing the Aircraft Y at a low point coming straight in and approved Aircraft Y's departure with restrictions. Unfortunately; my CIC had also not noticed the Aircraft X short-final.Aircraft X initiated a go-around while short-final 'for traffic on the runway'; and I immediately sent him on an early left crosswind to de-conflict from the departing traffic. Short of ASDE-X; I will work to be more vigilant on my scan and not be too distracted from unusual situations. The baggage door conversation and the unnatural coordination with the adjoining controller. Being fresh off training; I am accustomed to trying to push traffic as efficiently and expeditiously as possible with the 'safety net' of my trainer behind me but am realizing that I can now tone it back to a slower and safer but still efficient level of operations now that I have certified.