The Sopranos has an episode more or less about this, Commendatori. It's basically the glorified crew visiting their "home" in Italy and being your run-of-the-mill american tourists. Some interesting stuff is Paulie asking for pasta and red sauce because he doesn't like the fancy seafood he's been served, and Tony complaining about "lots of fish" to Carm over the phone.
When they get home they immediately resume their LARP and say they felt "right at home" lmao
The sopranos is a fictional dramatized soap opera though, made for a primarily American audience who are already vaguely aware of the "clash" between Italian Americans and Italians.
My "greek" side of my (american) family goes to Greece 2x a year for weeks, speaks greek at home, primarily eat a mediteranean diet etc. When I think of them, I think of "my greek family", and it certainly isn't some vanity thing.
When they get home they immediately resume their LARP and say they felt "right at home" lmao