Oklahoma City is unique in that most of its suburbs are in the city limits. The urban core is democratic, but its suburbs are similar to those in Nashville (white, evangelical, etc.)
This. Keep in mind that in 2020, Oklahoma City (Trump+1.6) actually voted to the right of Oklahoma County (Trump+1.1).
Yes, but Okla. City in Okla. County was Biden +10. The only reason the above is true is that OKC suburbs within Okla. County were more Democratic (or rather less Republican) than the parts of OKC in other counties.