I'm not going to argue that these things are completely orthogonal, but as the current inflation crisis illustrates, we can have steep inflation and high labor

I'm not going to argue that these things are completely orthogonal, but as the current inflation crisis illustrates, we can have steep inflation and high labor participation (of course, sustaining that labor participation in the midst of steep inflation is infeasible, but most people aren't economically literate and even professional economists get it wrong with troubling frequency).