Carmy knows Sydney is unhappy. He knows it. People who suffer from anxiety are usually very perceptive and sensitive to others moods as you have to be. He always knows when something is bothering her.
SHE WAS THE FIRST PERSON HE APOLOGIZED TO WITHOUT ISSUE. He had no problem doing this as he knows he broke his promise by fucking up. "I left you alone." He can't get over it. He has to make it up to her by getting that star, but he knows he's not doing it right.
He knows she's upset, but can't figure out what to say to her because he broke his promise to her and will not give himself a break because of it.
Claire is a part of his despair, but really it's Sydney. She's his blindspot and he hasn't realized he really doesn't want Claire. She isn't his dream girl. He can't stand that he and Sydney aren't on the same page. For him, Everything is about the kitchen. What he said to claire was fucked up, but it's also kind of true.
He made it clear this season. The kitchen is where he's happiest, most present. Until now and that is because he fucked up with Sydney.
He wants this back. He's reaching in the dark and can't see shit. Some of his longing stares at Sydney mean "This is what you want. I'm giving it to you, why aren't you happy?" while literally asking himself the same question. "You have what you want, why aren't you happy?" It's a terrible feedback loop of repeating trauma. He's happy in the kitchen, with Sydney. Now, as punishment for leaving her alone, he's shutting her out of vibrant collaboration which is making her be distant thus affirming his belief that he doesn't deserve happiness.
He's choosing Sydney over Claire, but also not choosing Sydney because he doesn't feel he deserves. Ugh!
Or I could just be completely wrong and if so fuck the writers of this show even though it's a fucking good show. WHAT DO WE THINK GUYS?