Interestingly, the more generous unemployment and social benefits are, the higher the employment rate typically is. The correlation is actually pretty strong. (Note: the table lists employment rate by the OECD measure, ages 15-64, whereas the BLS figure cited in the OP uses ages 16+ including retirees.)

While perhaps paradoxical at first glance, it makes sense if you think about it, since a more inclusive society also makes sure fewer people become detached from society, and more generous benefits also enable a more flexible labour market.

In this sense, the employment rate dropping at the same time the (already mediocre) safety net is being dismantled in the USA is unsurprising. It isn’t because of an innate lack of “jobs,” but because fewer people are in a position to be able or willing to work jobs.