[...] I wonder how much of these numbers for jobs are being affected by the growingly successful purging of workers that are in the US illegally....?
I'm going to speculate few to none. The second Trump administration claims to have deported about 140,000 people. That doesn't square with a loss of 911,000 jobs.
There might be some job-loss due to undocumented workers being deported, leading to labor-costs rising, and resultant shrinkage in the job market. But 911,000 jobs? Doubtful.
I wonder if over a period of time as actual US citizens start taking back jobs, say like in construction...if this will start to balance things out a bit....?
It needs to be said that there are plenty of legal workers in the USA who are not citizens, but who are instead permanent residents, are on various work-eligible visas, or are refugees with temporary status. Let's not try to equate work eligibility with citizenship exclusively, h'mkay?
And my guess is that some legal US residents may fill whatever jobs the undocumented deportees had to abandon. But I doubt there'll be a rush, because many of those jobs pay poorly and US residents don't want them.