It would seem he got it exactly in reverse: the vacancies are up because wages are too low compared to the demands of the labor force which is still available,

It would seem he got it exactly in reverse: the vacancies are up because wages are too low compared to the demands of the labor force which is still available, those people prefer to retire/have a baby/a sabbatical etc. etc. instead of working, because the price point being offered for their time is not attractive. Reducing wages will not solve this problem, but exacerbate it. What he's actually doing by increasing interest rates is reducing agregate demand, price action goes down, labor demand and vacancies drop and consequently businesses can pay lower wages without fear of losing employees. So the interest hike is a direct action against inflation while the wage drop is a side effect, not the intended mechanism of action. Inflation can be controlled via interest rates even if, say for contractual or legal reasons, wages stay up. Unlike the case of a recession - that is prolonged by inflexible wages on the way down.