And not just Captain's braids on his sleeves but the insignia of a completely different ship, station or Starbase on his breast. That tells me that in the original, unchanged timeline between the tragedy at Tycho IV and TOS that Kirk was either Captain of a Farragut or another ship with a completely different insignia or this is more time travel or alternate reality shenanigans.
I actually think it is the badge Commander Hansen was wearing in “The Quality of Mercy”. Maybe Kirk is commanding some type of facility at this point.