Yes. Professions where you can walk off the job and find a dozen other ones that have openings (say, software engineer) get much higher wage increases than one

Yes. Professions where you can walk off the job and find a dozen other ones that have openings (say, software engineer) get much higher wage increases than ones where if you walk off the job you have a very limited set of other employers (say, geologist or elementary school teacher). That's why you have a very bifurcated set of anecdotes, where some people are like "my COLA was still a measly 3% this year" and others are like "I switched jobs for a 20% raise."