It seems so, here is one study from the Chicago Fed, by Kristin Butcher, Lucas Cain, Camilo Garcia-Jimeno, and Ryan Perry:

Standard estimates based on the main household survey used to shed light on labor markets—the Current Population Survey (CPS)—suggest that after a significant drop during the pandemic, recent rapid growth has brought the foreign-born population back to, or above, levels predicted by the pre-pandemic trend. However, we document that the weighting factors used to make the CPS nationally representative have recently displayed some unusual movements and conclude that standard estimates of the foreign-born population may currently be too high. We also show that recent labor market indicators are inconsistent with increased foreign-born induced slack.

Ive also read some privately-produced Zonda research, with a letter from the U.S. Census (neither on-line), basically supporting this conclusion, in the range of 1.7 million to 2.2 million.  So the current foreign-born population in the U.S. isn't near as unprecedented as some people would like you to believe.