Speaking as an immigrant who is now a US citizen, I don't think this is particularly relevant. As far as immigration support from companies goes, Big Tech already offers it, so the real beef is with the federal government - and a trade or company union is hardly the best venue to have that fight. I would first and foremost want a union that protects my interests as a worker against my employer's encroachment, and it was no different when I wasn't a citizen yet.
Congrats. But the top priority for a non-citizen immigrant would be protection, above employer encroachment. Notice how this played out when twitter fired 85%, and who stayed back.
Unions being political players will have to take a side - and in the current climate this makes unions a non starter, since majority can never align.
As you can see, your bosses already did.