So the absolute resistance depends on the doping, which is tricky enough to control (furnaces, impurities, voltages, sputtering, etc.) that even with good control, the final resistance is within 20-30% of the target.

The relative resistance comes from the shapes themselves: it's the same material for both resistors, with the same properties from the same doping. And photolithography is great at matching shapes and patterns, so you get fantastic relative tolerancing.

There are, of course, still plenty of other sources of error.

It very much is a basic technique you learn in analog circuit design (or at least it was 30 years ago when I was in school). Similarly, there are circuits (like that current mirror) which rely on the nonlinear behaviors of diodes or transistors varying in sync — you can build them on the same chip, or you can carefully select matched sets from one manufacturing run.

An example with resistors is a voltage divider. The output voltage depends on the ratio of resistances not on the absolute values (within reason). The resistors in a long-tailed-pair also need to be matched but their precise value is less important. Or you might have a bias current that's temperature-dependent but in a way that matches the temperature-dependent needs of some other bit of circuitry on the output.

There's a famous early integrated opamp which has a four-way-symmetrical die layout to compensate not only for temperature variations across the die but also process variations.

It is well known. "Matched components" are common in analog design. (No two things are ever identical, but things fabricated next to each other are more likely to be much closer, and you can get better tolerances if you're going for a specific ratio.)

As a simple example, a voltage divider has the output voltage depend only on the input voltage and ratios of the resistance values. Vout = R1/(R1+R2)*Vin https://en.m.wikipedia.org/wiki/Voltage_divider