> I've met many people on my travels who went to Europe on tourist visas, got work and then got to stay legally later.

That's completely legal for some nationalities, at least in Germany. §41 AufenthV allows people from certain countries to come to Germany and apply for a visa there.

A separate paragraph allows people to convert a tourist visa to a residence permit if the reason for the residence permit appeared while they were visiting. For example, going through rounds of interviews, and being offered the job while you're visiting Germany as a tourist.

There are so many other paths, but navigating those options can be confusing.

The problem is, that only works if your Aufenthaltsbehörde isn't swamped in case load. Unfortunately, the ones in cities where tech workers are wanted are swamped and often times you need a lawyer to file an Untätigkeitsklage (inactivity lawsuit) or threaten to do so to get them to respond.

The Ausländerbehörden are massively understaffed (well below 50% of what would be needed), and work distribution usually is that anything attached with a court deadline has absolute priority, anything from a lawyer comes next, and whatever comes from a generic person or company just gets shifted to "Ablage P" (the paper recycling bin).