Unemployment isn’t that high, people who don’t work at the moment don’t do so out of choice (because clearly unemployment isn’t the best way to pay rent!) and we’re talking about redistribution of wealth in all sectors, not just that one sector, so all wages would increase. You don’t end up with more workers suddenly wanting to work construction (which are already well paid jobs in most locations which doesn’t seem to help recruitment!), you still have the same unemployment rate and the same labor needs, you just redistributed wages in a more sensible way.

Hell, demand would probably increase in most sectors due to the general population having more money to spend instead of it being in the hands of so few people, that means more people required to make stuff without having more people to take those jobs!