As far as I can tell, the poorest workers' real wages grew, and grew faster than the median workers', on a relative basis, from 2019-2023:

https://www.epi.org/publication/swa-wages-2023/

Yes, the simplistic "immigrants are competion" narratives always disregard the fact that immigrants also contribute to the economy and uplift it. For instance, there is a credible theory that the "immigration crisis" was instrumental in managing the inflation crisis: https://fortune.com/2024/04/12/immigration-inflation-economy...