May this variable be a proxy for race (non-White) rather than country of origin, or perhaps there are some intersectional dynamics here. For example, non-Western immigrants can be White. Western immigrants can be racialised. Haven't read the paper but discourse in many immigrant studies is bivalent.

Certainly. The experimental variation is by first name, which (in their data) is 0.89 correlated with ethnicity. But the experiment doesn't explicitly separate out the components of an ethnicity effect, like a race effect and a country of birth effect.