Not all. Some provide a stipend and/or housing allowance. Depends on the program and the agency running it.

Congress now pays their interns too, though I don't know if this extends to campaign interns: https://cha.house.gov/member-services/house-paid-internship-...

Political interns, no clue. However if you're working for the government and not a campaign, then you're almost certainly getting paid in the US.