This thread has been an interesting read for me - I'm also from abroad and have settled in the West Country with my DP (who is from here).
I think PP are probably right about them trying to "place" you... DP sometimes tells me that I'm "lucky" I'm not British because people can't place me easily - whereas they jump to conclusions about him within seconds of him opening his mouth.
Sometimes, very rarely, I get some gentle prodding questions about my parents, schooling, background, etc. that are clearly attempts to "place" me. However, this has always been done in a classically British, low-key way, and no one has ever opened a conversation with it. It's kind of a roundabout, "so did you also play a lot of sports in school like your DP?" to try and figure out what kind of school I went to, or a "so do your parents also do X, or what made you want to go into the industry?" OK, on second thought, maybe not THAT subtle, but a far cry from outright asking if I own houses abroad, or starting a conversation about pay rises!
That said, in other places I've lived, people have also tried to "place" me but are WAY more direct about it. In my home country it's not unusual to get asked how much money DP and I make in England, how much our house cost, how much our car cost, etc. etc. It's so awful but you have to laugh, which actually reminds me that I need to get some "answers" ready for when we go back next month😂So in my experience, the good people of the SW are by far not the worst offenders...