uhhhh.... no
The galaxy dosent collapse due to angular momentum

the nebula dosent collapse due to angular momentum

the neutron star dosent collapse due to neutron degeneracy pressure

the black hole does collapse because the gravity exceeds neutron degeneracy pressure

for stellar mass black holes, the hawking radiation is miniscule. Trying to get energy from hawking radiation is kinda like trying to heat your home with rusting steel. technically, it is possible, but the quantity is so small it isnt really helpful.

As for how to extract KE, try a sail. the particles from the hawking radiation will bounce off and give you a net increase in energy.