I don’t think this captures the full story. The US has a bimodal standard of living reflected as a lower mean relative to other advanced nations.

It can be simultaneously true that immigrants to the U.S. from both advanced and developing nations both experience a higher standard of living than their countries of origin.

Immigrating to the U.S. with an advanced degree in an in-demand field: you likely will experience a higher standard of living.

Immigrating to the U.S. from a developing country without a particularly in-demand career: you likely will experience a higher standard of living.