A Tower Controller reported an aircraft initiated a go around after being issued a low altitude warning. During the go around they received a TCAS/RA for VFR aircraft operating 500 ft. above their assigned altitude.

Narrative

Aircraft X heavy elected to do a go around after issuance of a low altitude warning on approach. After issuing instructions; I called to approach to coordinate a heading for the aircraft before shipping communications as is a standard practice. At the time aircraft was on a 180 heading and climbing to 040 per our LOA / SOP for that Runway. Approach Controller instead of issuing a heading began to berate and argue that the heading was incorrect due to construction on the airport and current traffic flow. No coordination contrary to SOP had ever been done to reflect this. Due to the poor communication and distraction of the attempted coordination; no traffic call was given to Aircraft X about the VFR overflights at 4500 ft. on another frequency. Aircraft X responded to a TCAS RA due to climb rate. No separation was lost but fit was an unnecessary occurrence that could have been prevented. Controllers need to be aware that in the middle of a high workload situation such as coordinating a go around; distractions by berating a fellow Controller over a perceived mistake does not contribute to a safe controlled traffic environment.