As fucked up as it is, judges depend upon the executive branch to enforce court decisions.
When a federal court imposes contempt sanctions, the U.S. Marshals Service enforces the order, including arresting persons ordered imprisoned for contempt.
The U.S. Marshals Service is an executive branch agency within the DOJ.
https://www.uscourts.gov/about-federal-courts/court-role-and-structure