Claire is Carmy's projection of Sydney.

Costuming is one of the most straightforward ways to tell an audience what a character is like and what their role is. Claire's costuming choices show how she was literally just a clear blank slate for Carmy to project Syd onto. So come peel this onion with me.

When he first sees her after being away from him for a while she's wearing a green jacket, who else famously has worn a green puffer jacket all throughout the series and when she reconnected with Carmy after she left?

When he takes Claire on that post office trip drive through Sydney's favorite UPS route, Sheridan Road, she's wearing a brown jacket which looks very similar to the kinds that UPS drivers like Sydney would wear.

When Claire is at the party with him trying to get with Carmy and pursue a new relationship, she just had a denim jacket. Which we have also seen Sydney wear a denim jacket around him when they were trying to start a new relationship aka partnership together by building the new restaurant.

And then we see her white button shirt, dark pants, and the blue denim jacket when Carmy takes her back to the restaurant, which is basically all Carmy saw Syd wearing for most of the time while at the restaurant when she was in her white button down, dark pants, and blue apron.

When he cooks for Claire we see her for the first time in a tank top at the exact same time we see Sydney the most undressed she's ever been in a bra.

When she's in his kitchen she's in his white t-shirt she tries to have a somewhat vulnerable moment with him. She asks him what he is thinking about when he's clearly stressed and he deflects to just complement her. Later when he is with Syd in her white t-shirt in their kitchen at The Bear, he is vulnerable with her about his mother and tries to get her to be vulnerable with him and she finally tells him about her mom dying.

At Friends & Family night is the one time we see her dressed in the most uniquely herself way in a black dress, and she looks like she's ready for a funeral. Which it essentially was the death of her and Carmy's relationship that night. We also know that this is what Sydney will be doing at the start of Season 3, going to a funeral with Carmy. RIP Claire. (yes i know it's marcus' mom but the metaphor is still there and this is still a comedy after all)

Claire has very little identity of her own because Carmy never bothers to know her like he knows Syd. When Claire is on her own she's always in her scrubs, because he doesn't have much else of an image of her besides the fact that she's a doctor now. But he knows Syd well enough to know the exact designer brand she likes to wear and make her a custom jacket.

He knows about Syd's mom dying because he repeatedly asks her about her family and parents without even knowing them. Claire told him about her cousin dying and he basically said "damn that sucks" even though he knew him personally. He knows about Syd's struggles with her job history through catering and fine dining. Claire told him about her life as a doctor and the only thing he came out with was that it was a time intensive job and that he thought she liked taking care of people by helping to fix them. Which is exactly what he tells Sydney he notices about her later on. She likes to take care of people and to fix things like she tried to fix the restaurant.

He didn't give af about Claire's life or personality, he just wanted to project Sydney's onto it. Carmy wanted to want to be with Claire, because everyone around him told him it was what he should want from Mikey to Fak to Richie. So he chose to see and project as much of Syd, who he already knew deep down he liked but was too scared to pursue, on to Claire. That's why he took her on that drive and why he made her the Sydney's pasta recipe that he knew Sydney already liked. Because he doesn't bother getting to know Claire, he just assumes Sydney's identity on to her. And what he did come to know and do with her that was her choice, like going to a party with drunk friends, only ended up associating her with his alcoholic mother and his brother at their Christmas party.

And in the end he still realized he couldn't just replace Sydney in his mind with her.