Which would lead to the question, Why is Kirk's yeoman wearing red? Maybe she is pooled from—or a part of—Security?
That's a good point. Rand wore gold in the publicity photos. Maybe they just thought she looked better in red? But then that breaks the system. She is an engineer in TMP, so maybe she was trained as an Engineer. (Of course in TMP she wore gold with red insignia...)
TOS ranks between ENS and CMDR are "naval ranks - full stripe" so ENS lose their one stripe and LT-JG go from one full stripe and one half stripe to a half stripe; LTs drop from 2 full stripes to 1, LT-CMDRs drop from 2 1/2 to 1 1/2, and CMDRs drop from 3 to 2. What doesn't make sense is the TOS CAPT striping, which should following the same pattern be 3 full stripes (down from 4) not 2 1/2.
NB: There is a some precedent for both 3 1/2 stripe "captains" (which logically is what Kirk is during TOS and Pike was at retcon'd into via DSC) in the RW, and for a 1/2 stripe, typically given to either cadets/midshipmen, but occasionally very junior officers (roughly corresponding to US ENS).
If you sort of "re-calibrate" your system from "real navy rank minus one stripe" to "ensign=0 stripes and add 1/2 stripe for each rank," then 2 1/2 stripes for Captain would make sense. Interestingly, the TNG pips do not seem to have the corresponding "3 gold 1 black" pip configuration, which arguably could have been what Riker wore when "field promoted" to captain.
Looking at it from a 1966 perspective, without the manuals to tell us otherwise, I could say that Kirk is a captain (position) with the rank of LTCMDR, Spock wearing only LT stripes having taken a temporary grade reduction so as not to outrank the captain. This would have to apply to Scotty and McCoy later, but their ranks are not spoken in dialogue right away. Kind of a stretch but interesting. If we really wanted to push it, Pike could be a LT in charge of the then-smaller ship, with Number One having taken such a grade reduction.