I have heard about the experience in Seattle a couple of times an I believe that people are commenting on a study conducted last year that did show that found:

The change made low-income workers worse off, not better, because it forced employers to cut back on hiring and hours to afford paying higher wages.

However in this article it describes a paper which contradicts the first paper underscoring its limitations.

The second paper found that eliminated minimum wage jobs were replaced with better paying jobs.

Dube's paper is more in line with conventional economic thinking: On average, minimum-wage increases eliminated jobs paying below the new minimum, but added jobs paying at or above the new minimum. The two changes effectively cancel each other out.

You described what the expected outcome yourself:

I've experienced price increases and staff shortages in my area

Businesses respond to the increase cost of labour by increasing their prices. Because people now are earning more, they are buying more. Businesses respond to the increased demand for their products by hiring more people ... spurring staff shortages.