That second-year episode is the only live-action one where Uhura should clearly have been in command. I'll agree that DeSalle was promoted THEN for real-life societal reasons, but I don't believe for a moment he was fifth-in-command in THE SQUIRE OF GOTHOS. Has Nichelle Nichols ever commented about this?
Uhura was a "lieutenant," but this was a ship full of lieutenants, and they were seldom seen to have any subordinates. I think there was some title inflation going on.
In TWOK, Saavik was addressed as Lieutenant despite still being an Academy trainee. It's not like our current Navy at all. The rank of lieutenant just doesn't mean much in Starfleet. It's like having a yellow belt in judo.
There is scant little in-universe edvidence that Uhura and Sulu had any power; they never even gave Chekov an order. The animated series would later portray (retcon?) Uhura as a ranking officer, but not TOS.