It was never meant to happen, right?
It clearly hasn't worked out by TOS (and isn't really touched on in the movies) but perhaps there is a future beyond TOS.
Then, once Korby was gone, she was back to "mooning over"
The order in which the episodes aired established that she held those feelings while still searching for Korby. As it aired this way, I assume that this is what the writers are working with so I don't think she leapt between men so much as consistently held onto feelings for Spock.
The fact is that Spock is hurt. Very hurt. And the only way for a Human/Vulcan hybrid to deal with that kind of pain is to close oneself off.
I think that the hurt would have made more sense if they'd had a successful, established relationship first. That made it quite unsatisfying to begin with as Christine clearly wasn't prepared to even call her time with Spock a relationship. The intensity of the hurt would have made more sense if they'd spent half of season 2 and the first half of season 3 as an in love couple.
I appreciate that they wanted a reason for Spock to become so closed off but that level of distance was partly due to Spock being TV alien in the 1960s and a bit one dimensional. This Spock is more emotional and dynamic as this is a modern take on on the same character. We can't really explain Chapel's personality transplant as her being younger, she's clearly a modern take. I don't find it entirely believable that this Spock will close himself off to such a close friend let alone other friends such as Uhura. I also can't believe that Christine wouldn't work very hard to maintain or rebuild that close friendship. Spock wants and needs close relationships even if they aren't romantic as it's clearly important to him. Would he really be all or nothing with Chapel? This Spock doesn't seem SO hurt that he would cut off any contact and friendship with her.
Your post makes me wonder about the autobiography that Boimler mentioned. I'm curious how the writer's will make sense of Christine not being mentioned. She's clearly very important to him. Will they go down the road that she broke his heart so thoroughly that he never wanted to mention her?
Her face when she was asked to tell the "romantic story" when Spock was standing there and also when he turned and left did not tell me that she was cold. She's still in love with him, but she's pushing him away bc she now knows she's not what "his future" needs.
I wish that they had included a scene of her saying this to Uhura and La'an. It would help connect the two seasons. The vibe from the episode is that Korby is the best choice for
her and she's over the moon. It would soften the situation is this was least partially about what's best for Spock. It would equalise the pain and hurt a bit. I hope that they include some sort of scenes like this in future episodes this season. The 'still in love' part needs to be clear to line up with TOS.
Still, I'm happy to hear that not everyone felt that she was cold. Perhaps I've had a very harsh interpretation. I would hate to be Spock in this situation and not given advance notice so that I could make a choice about making myself scarce. He's had no warning and I think she owed him more than that.
Sadly, I think we know the ending on this one as well.
I can reassure everyone that yes, I have most definitely watched TOS

. That's why Christine's total lack of feelings doesn't line up for me as she is clearly in love with him (still? again?) by TOS.