The legislature is a separate branch of government. I assume that also means congressional staffers are also paid. The “government workers” (All executive branch!) not being paid are the ones with the least to say or effect it.
Ok looked it up! Staffers may or may not be paid its up to Congress. Congress is paid no matter what they do or might want as dictated by the 27th Amendment (Summary: Congressional pay can’t be altered during a session!)