All right, has a small postive effect on native wages in aggregate, as the paper I sent takes pains to point out.

One important caveat is that we analyze aggregate labor markets and not individual workers’ outcomes which are not observable in our data. Some individuals may be displaced from work or experience reduced wages due to the competition of immigrants. The differences in individual outcomes and outcomes for the aggregate labor market in response to immigration were also pointed out in Dustmann et al. (2017) and Foged and Peri (2016). Still, our average outcomes suggest that for any group of native workers dropping out of employment or experiencing lower wages from immigration, a larger group of natives are attracted into employment or experiencing increased wages.

The point being, increased competition in a given sector will lower wages, obviously. But, all that's really doing for the tech sector is drawing forward the natural balancing of supply and demand that would've happened through education, anyway.

Also, the study does take into account illegal immigration to the US.

As for your example of Canada's highly unethical immigration policies. We agree! Importing workers and denying them mobility leads, basically, to a caste system where it's more profitable to hire the lower caste. The solution here is not reducing migration, it's to ensure that all migrants have full legal working rights. Either you're in, or you're not. In between statuses are bad both for the migrant, and for the native working class.

https://publications.iadb.org/publications/english/document/Illegal-Immigration-Border-Enforcement-and-Relative-Wages-Evidence-from-Apprehensions-at-the-US-Mexico-Border.pdf