T'Pring looked a lot different in TOS S2 - "Amok Time"...


^^^
(Yes - that's my story and I'm sticking to it.)
Look at TOS S1 - "The Menagerie" now. I mean hell, if Uhura served with Pike as we're now seeing - you'd think she'd be more interested in saying SOMETHING to him/visiting him once she knows he's been beamed aboard the Enterprise when Spock addresses the crew; and she's there on the Bridge when Spock says to McCoy he's just to take good care of Fleet Captain Pike.
I don't technically think there is an issue with either.
In the Menagerie, Pike doesn't seem to be wanting visitors when we first meet him. His trauma might make him very upset it seeing sympathy from others (It happens quite often in real life). When he comes aboard there are orders to leave him alone. Now that might be from being kidnapped, bu that would be difficult for Chris to express, there could absolutely be an aspect of that choice due to Spock being aware that Pike doesn't want company. And after that we only see him in the trial. That trial doesn't seem to have an audience we see only the required personnel for the proceedings. The judges, Scotty running the tapes, Spock, and McCoy (I assume to monitor Pike) and security forces for the prisoner.
We don't see Pike for all the time he is on board the Enterprise. AS such who knows what occurred during the hours where we the audience don't see him. There is a hue amount of time that Uhura or Chapel could visit Pike. In fact for it to be even an issue we would have to have dialogue that specifically states that Uhura never went to see Pike. No such dialogue exists in Trek. And even if she did state that, of course there is a possibility he didn't want visitors and she choose to respect his wishes. So there has never been an issue with this.
Now with Amok Time, Spock never describes T'Pring as his wife to her. And I assume she is shocked because Spock has (under the influence expressed desire for her). She very well might be surprised that's the case, if he was a married man, versus one who isn't yet married.
Another one during this episode (for me) was the mentioning of the Romulans, and I thought at this time the Federation hadn't had contact with them (which they hadn't), but I forgot this information was provided by the race that they were in negotiating with. We have no dialogue indicating that the Romulans didn't go outside their territory or have diplomatic relations with non Federation worlds. Or for that matter, this race might have just been lying and throwing the name Romulans out there to strengthen their hand.
5 episodes in for me this is easily the best start to any Trek series 8 or higher across the board