Except this is literally false. Every single study I’ve seen that claims this has no real evidence - just speculation without knowing the details of the jobs or the people being hired, based on their own self-serving false comparisons to make dubious claims that similar jobs are paid differently.
Since you said “across the board”, do you think Google or Amazon pay a software engineer at the starting level differently based on immigration status? No, they don’t. Literally every manager at big tech could tell you this confidently.