Your compensation isn't driven by the things it can buy. It is driven by the balance of supply and demand in the labor pool, which is mostly insensitive to inflation in the short term.

In the long term, sometimes inflation is caused by employers being able to charge more for their products. If they can raise prices faster than their costs, then they'll be able to afford more folks to work, increasing demand in the labor pool, hence increasing labor prices (i.e. compensation).

Still, it can take several quarters for information about pricing to flow through the supply chain and impact wages.

There's also the fact that the "inflation rate" is a pretty imprecise number. There's no real inflation rate, it's more of an average of the price increases of various sectors of the economy. But even drilling down into the sectors you have to account for things like geography. So the inflation rate is useful as a gauge for where the economy at the macro level is heading, but for making individual salary decisions at a single company it's not very helpful.

it's really not. in fact there are specific terms to differentiate them

cost of living is your total live cost including inflation. cost of labor is cost to hire replacement in the overall labor market.

most companies pay in each market based on cost of labor

Depends on the demand for your skills, not generic inflation.