This isn't exactly new territory. A lot of countries are very careful to avoid letting you in on a tourist visa if you give off the appearance of entering to work.
I'm sure there is more of this than in Europe than I'm aware of (food delivery is one example we're recently had a lot of focus on in the UK) but it's certainly not at the point that it's routine and expected.
How does this work? Are these people somehow paying taxes regardless of their immigration status?
Also in states like California they let undocumented immigrants get drivers licenses. They can even get bank accounts and mortgages in some states (which is basically impossible here in Canada).
Some jobs are cash jobs, the employer doesn't report the income and the employee likely doesn't either, this isn't legal for the employer or the employee, but enforcement is uneven.
For jobs with proper payroll, income reporting and employment tax withholding, it's common to 'borrow' someone else's tax id. That's not legal either of course, although the employer may be ok if they were reasonably unaware of the borrowing. If the borrowed tax id is only used for work by one person, and the withholding is close to correct (or a tax return is filed for that tax id), then taxes are being paid properly, even if they're attributed incorrectly. If the tax id is used by multiple people, then the combined income might be subject to a larger tax than if earned by multiple tax ids, and withholding is likely to be iffy (withholding tables are built around a single job).
I think I've heard of ways for someone without work authorization to get their own tax idea so they can have make properly attributed tax payments, but I don't remember the details.
This "Yooz Brok Duh Lah" absolutism is a transparently political excuse for what is very obviously a norm-breaking and unjust enforcement of a law that was working very well.
OP was asking how there's huge communities of undocumented people in the US and how they manage to work and live without legal status. Which would be an unusual thing in almost any country. The logistics of doing so is a valid question (how do you drive to work, how do you find housing, how do you get healthcare, etc). The answer is many state and federal policies support having millions of undocumented people in legal limbo indefinitely, by offering them pseudo-legal status or loopholes.