Yes, I think it is generally true. We have millions of criminal aliens in the country now, and the Covid funds are gone for citizens, but the worker shortage is acute.
I published something a couple days ago about how .. I think it was 1.5 million jobs had to be "retracted" back to last june/july, as the government only now (coincidentally) discovered its math error. And then there are all sorts of bureaucratic fudging which go on all the time to keep us in line, more or less, with Our Masters designs.
I believe that disabled workers are not counted. And those who are unemployed but no longer "looking", or who have simply been looking too long (and 2020 is way too long) are - conveniently - dropped from the calculation (must not be unemployed if they are still unemployed).
Anyway, I expect the real number of “disappeared” is probably MUCH larger than the 3 million you mention. And I believe there are multiple contributing factors.
I fear 2023 is going to be one hell of a year if the last month has been any sort of prelude.