what do we call protests in which people sit down someplace and refuse to leave?

Those protests are called sit-ins.

Quick Scoop

When people stage a protest by sitting down in a place (like an office, restaurant, or campus building) and refuse to leave, the classic term is a sit-in. It is considered a form of nonviolent civil disobedience, because protesters occupy a space peacefully to pressure authorities or owners to address their demands.

Historically, sit-ins became famous during the U.S. Civil Rights Movement, when activists sat at segregated lunch counters and refused to move until served or arrested. The power of a sit-in comes from its visibility and the moral contrast: protesters remain passive while any attempt to remove them can look harsh or unfair, which often increases public sympathy for their cause.

TL;DR: The protests you are asking about are called sit-ins.