Lol I'm American and had to Google "UK seven classes" b/c I hadn't heard that. The British class system is wild to me. America definitely has a sense of new money vs old money and obviously a lot of racial class tension rightfully so but it's far more cut and dry than a seven class system. From my vantage point I'd say by American standards Carrie was raised (American) middle class and is now (American) upper middle. I consider myself the same.
I went to a private middle school (US grade 6-8, age 11-13) and I recall that gut feeling of "These people have more money than I do." My classmates would mention their cleaning ladies and talk about their international summer vacations. During birthday parties and sleepovers I noticed that their big houses were in nicer neighborhoods than my house was in. And, I will admit, at the time I felt quite poor in comparison. Then I went back to public school for high school and suddenly felt quite wealthy compared to the kids who would ask around for a dollar to get home on the bus.
I think if Carrie had gone to University/ Drama School it might have humbled her in the same way: Living in student housing, meeting tons of people working waitressing jobs between classes, maybe having to get one herself, etc. Her path to success was fairly unorthodox: YouTube due to being the right age at the right time, getting a book deal b/c Gi had a book agent b/c Gi was married to Tom and Tom was famous, getting a West End principal role as her first professional role, buying an apartment at 22, buying a house at 26(?), etc. I think she lacks some crucial empathy for her fellow actors who are baristas, dance teachers, office workers, who started in the ensemble and worked their way up.