The whole point of the omelet scene with Sydney is the care she took with it, as expressed in the time and technique she was using when nobody was looking. Sugar was pregnant and hungry and asked for an omelet. Sydney was not serving a customer and was not being judged or evaluated on the omelet. She could have just banged out a perfectly edible omelet and Sugar would have eaten it. So why loving beat the eggs over a mesh strainer, perfectly execute a french omelet (I won't go over all the steps, but the show nails the details with how the french omelet is executed - no disrespect to the photo posted up thread, and make no mistake I would gladly devour it as it looks delicious, but that is not a french omelet technique with how browned the omelet is), put in the little touches with chives and crumpled chips, and make sure to even coat it one last time in butter? Sydney did that 1) because she loves to cook for cooking's sake and 2) she loves to take care of people.
One of the big themes of this season - especially in the second half of the season - is about the motivation of why we work, and in particular making the case for the beauty of working from a motivation of love and service.
Marcus - goes to Copenhagen, learns a lot from the pastry chef. The pastry chef tells a story of how he thought he was the best until he met someone better while working as a commis (strongly implied he is talking about Carmy when, in the Fishes episode, Richie walks in a hallway and sees a picture of the pastry chef and Carmy). Pastry chef talks about how he had to learn that it isn't just about mastering technique, the best dishes he had ever eaten were inspired. Marcus is tasked with coming up with three desserts and nails it, inspired by Copenhagen, Sydney, Carmen, and Michael. Marcus creates out of love.
Sydney - see omelet example above. She is weighed down by doubts, fears, responsibilities - but at the end of the day she still loves to cook - it comes from a pure place. She might want the stars and she certainly wants to reach financial stability (not bad desires!), but underneath it all, she is motivated by love of cooking and love of serving people.
Richie - the most dramatic arc demonstrating the theme. Richie is angry and defensive and doesn't know his place. He is good with people but torpedoes whatever progress he makes due to his personality flaws. Through his experience staging at a 3 Michelin star restaurant, he comes to see the beauty and dignity in serving others. It transforms him and allows him to hone his strengths without self sabatoge.
Sugar - her involvement with the restaurant started as a place of conflicting feelings for her, with all the ghosts and family trauma associated with it. At the beginning of the season, Sugar said at first she couldn't stand to be there but, once they started the renovation, she felt herself drawn there. She starts out somewhat reluctantly part time, getting drawn more and more into it. By the end she has discovered she is good at project management and loves/is invested in the success of the restaurant. She navigates issues with the city, staff, Carmy, and Cicero with skill. In the last episode her husband affirms the changes he sees in her, saying how happy he is and how much easier it is to live with her now that she's found something she loves, even if it has required more of her.
Claire - hers isn't really a journey. She knew when she was young she was fascinated with understanding medicine and how to help people, as evidenced by her story as a child when a friend broke her arm. Claire has a very realistic and clear eyed vision for the sacrifice involved with residency and pursuing her passion/vocation, but she loves it despite the sacrifice. Claire understands that even though it is busy and draining, it is life giving to love what you do and help people doing it.
That leaves Carmy - he is the one character still figuring it out. He is in process. He has the training, the talent, and the accolades. Does he love to cook, or is it just something he discovered he is really good at? Did he press into cooking because he brother wouldn't let him be part of his restaurant, so Carmy set out to get so good his brother would have to let him in? Was he able to thrive in the intense pressure cooker of working under pressure and abusive chefs because he raised by a narcissistic mother? There is evidence that Carmy found refuge in food, discovered he was good at it, but never really loved it. There is also evidence that Carmy does love food and loves people. Carmy is constantly getting distracted - the fridge door handle being the obvious thing - but the entire season Carmy is dodging meeting with Sydney to focus on the restaurant. But Carmy, when present, also shows himself capable and willing to love and nurture. We see him gladly give up his knife to Tina (no small thing for a chef to do). We see him listen and take the time/effort to give Sydney a special chef coat. We see Carmy, with Claire's influence, start to confront his past and channel it into inspiration with the savory pistachio cannoli.
At the end of the last episode, when Carmy is locked in the fridge, he and Richie have an intense screaming match after Richie sees Claire leaving upset. Richie accuses Carmy of being just like his mother, which (understandably) sets off Carmy. Richie's point is that, like his mother, Carmy will not let himself be happy, will not enjoy who is around him and is constantly looking for the black cloud over every situation. Viewed a certain way, Richie has a point, but it is also somewhat unfair as Carmy - unlike what is depicted of his mother - is not a narcissist and shows himself over and over capable and willing to team up with others, look out for them, serve, nuture, and elevate them. However, there is no denying that Carmy is in a transitional place - there is a realistic scenario where he takes the Richie path, and a realistic scenario where he takes the path of his mother.