Another point to add is a lot of rich, white, educated suburbs in the south are resisting the trend due to high rates of evangelicalism in those communities. Especially if they’re not recently formed but long standing communities from the Bush era or before. Highland Park and University Park are examples of this.
I don't know if that's necessarily the best explanation for the voting patterns of places like Highland Park, Buckhead, East Memphis, etc. These areas are fairly evangelical but aren't generally hyper-evangelical in the way that southern outer suburbs and exurbs tend to be; the voters here skew mainline Protestant in my experience. Instead, imo, places like that are Republican, or at least less Democratic, because they're the homes of the traditional southern gentry.
The North section of Raleigh inside the Beltline is a good example; Democrats posted pretty paltry numbers here even in 2020, and Trump won a precinct near the Country Club in 2016. This area was where white people with money lived from the beginning, and because it's near the center of the city it remains desirable and has experienced little white flight (the fact that residential land use in most southern urban areas is generally suburban-type single family homes plays into this too). As a result, the area has seen fewer transplants and less development than demographically similar areas further outlying, which were built in an era where the affluent residents who moved in were new money, often from the north, and which have generally experienced more demographic churn.
This even shows up in language; the linguist Walt Wolfram, who teaches at NC State, pointed out in his book Talkin Tarheel that nonrhotic accents in inner Raleigh, unlike the rest of the state, are strongly associated with monied white speakers.
Durham is actually fairly unique for not having an area like this, because its rich areas are highly influenced by Duke University and so it has changed the particular local culture.
tl;dr: Basically these places are demographically more old school upper-crust southern than most of their metros, including newer and more outer suburbs.