definitely feels like "immigrant" is for white people and "migrant" is coded for Black and brown folks

Yes. And expat is reserved for the white immigrants with a substantial amount of money.

To me ‘migrants’ suggests that they will not be staying, where ‘immigrant’ does. Which I’m sure is how they would like to frame the situation with the immigrants from Haiti.

"expat" for higher income and whiter immigrants

For me, immigrant meant someone who'd come to live in a new country, while migrant meant someone who was in the process of coming to live in a new country. A migrant is on the move, an immigrant is here. I guess the language is used here to make them feel less committed to their community.

Immigrant is only for non-English speaking white people. The English speakers get called expats.

I think it's because "migrant" implies they'll "migrate" away at some point while "immigrant" is a statement that they're here to stay. And white supremacists do not want to accept that Black and brown folk aren't going anywhere.

In its xenophobic usage, "migrant" is the contemporary black & brown take on the medieval antisemitic “wandering Jew” trope - contrasting with the integrating immigrant.

expat = white immigrant

what does Rich Lowry call them?

I would say "immigrant" is for white people who don't want to be reminded that they're descended from invaders :-)