The establishment survey which is what reports the job numbers doesn't track if workers are native born or foreign born, let alone immigration status.
The household survey which is what reports the unemployment rate does track immigrant workers as a group, but not by status.
Ironically in the September jobs report native born workers had significant gains. The unemployment rate of native born workers decreased to 3.8% versus 4.2% for foreign born. The native born unemployment rate has been lower under Biden than it was under Trump.
There's been a persistent right-wing talking point the past few years that the job gains have been mostly among immigrants and not native born workers. But prime age native born workers are above their pre-pandemic employment.
It is making the all too common error of not adjusting for compositional changes to the work force over time.
If you don't adjust for the aging of the work force over time it can make it appear like native born workers aren't recovering. But native born workers are getting older and retiring over time. Older people tend to have lower labor force participation than younger people. It is why immigration is good for the economy.
One way to handle this is by looking at prime age workers as a group. That way your frame of reference is less sensitive to aging compositional effects.