If The Fed continues raising rates and/or doesn't lower them again for an extended time, all that MIGHT do is slow things down, and the end result will be an even bigger and faster stock market climb.
Inflation is already falling. The Fed needs to keep hands off at this point and just let the market forces do what they will (but it likely won't). As much as The Fed wants to slow the labor market, it can't physically produce workers. Baby Boomers are retiring and NOT even taking part-time jobs. Fewer immigrants came here because of the pandemic and (a TINY bit) because of that America First nonsense, and, what is overlooked by too many is that we had more than a decade of strong market returns, enabling tons of people to retire fully or retire early and not worry about having to go back to work.
Unless there is a change in the attitudes of young adult Americans wanting to have children, we will NEED to increase immigration here to keep up with the work demand...from doctors to computer programmers to service workers.