The airport may have a San Francisco address and zip, but it is physically located in San Mateo County, and I can't find any evidence they have ceded part of the county to San Francisco County. The county map on the San Mateo County government website defines the area as unincorporated San Mateo County. Also, major crimes at the airport are investigated by detectives from the San Mateo County Sheriff's office, and the San Mateo DA's office in South San Francisco prosecutes crime at the airport. Why would San Mateo County do all this if the physical airport location is in San Francisco County?
https://isd.smcgov.org/county-gis

Here's a Facebook video with a San Mateo County detective explaining the unique relationship between San Mateo County and the airport:
San Mateo detective video

To quote the detective, "San Francisco International is very unique. It's actually the city and county of San Francisco own and operate the San Francisco International Airport. However, it is based in San Mateo County, so because it's based in San Mateo County we have a unique relationship with the San Francisco Police Department who are contracted to patrol here at San Francisco International Airport." Further, "every single criminal case goes to the San Mateo County District Attorney's Office."

I stand by my statement that the airport is in San Mateo County.