It’s really up to each station’s discretion, kind of.
I had rounds where Cap didn’t want the blatantly traitor Bartender that killed 3 crewmembers because MuH MeTaFriEnDiNg.
At the same time, I had captains authorizing HOS beheading the clown because Cap got slipped.
Or HOS plain out killing an assistant for fucking with doors once.
As long as there’s no abuse of power, HOS can auth executions if it’s for the wellbeing of the station and if there’s enough proof for it.