You can run for any US Congressional office no-matter where you actually live, at least in GA.
A couple years back, Ossoff (soon to be Senator) ran in my congressional district, but he didn't live in the district. He promised if he won he'd buy a house in our district. Many people publicly denounced him for it. He lost, but of course moved on to bigger things. And in the end, 2 years ago, a Democrat, McBath, did win our district.
BTB, McBath won re-election and she did so by campaigning about all the favors she'd done for people, not on the issues.