Your point (I think) re unemplyment and BKE

Both teen workers and the self-employed are not captured very well in the government's separate survey of employers that is used to calculate the number of people on U.S. payrolls. That explains much of the disconnect between fewer job losses overall and the much worse unemployment rate.

The rise in unemployment was not spread evenly across the population. For those with college degrees, the unemployment rate fell to 4.7% from 4.9% in September, as the unemployment rate for those in management, professional, and related occupations slipped to 4.7% from 5.2%.

But the unemployment rate for production jobs, such as factory workers, jumped to 14.5% from 14.1%. The jobless rate for workers in construction, maintenance or natural resources industries such as mining rose to 15.5% from 14.3%