The U.S federal bureaucracy being referred to as the fourth branch of government could be true depending on the angle someone views this. From a recent news article The President and his cabinet will travel to multiple events and highlight how the IRA (Inflation Reduction Act) has saved money and cut energy costs. One might view the executive branch of the United States as only the President of the United States himself and that’s it, however the executive branch of government is much more. For example the President has a cabinet of members that he appoints and most of these cabinet members are the heads of the 14 major governmental departments that make up the executive branch. These major departments are comprised of sub governmental agencies. For example the Department of Defense would be comprised of the U.S military branches with the NSA and DLA. If a person is to take the question of the federal bureaucracy being the fourth branch of government at face value, then no it clearly is broken down and disseminated into compartmentalized areas of the executive branch, however if a person views how these departments run their own organizations and work directly for and with the President in an advisory role having almost a direct impact on how to shift the direction the United States is going, then yes the federal bureaucracy could be considered to be the fourth branch of government.
Sink, J., 2022. US climate-tax bill has Biden, cabinet mapping multistate blitz to tout win. Bloomberg.com. Available at: https://www.bloomberg.com/news/articles/2022-08-15/biden-cabinet-map-multistate-blitz-to-tout-climate-tax-win [Accessed September 6, 2022].
Anon, Official US executive branch web sites. Official US Executive Branch Web Sites – Newspaper and Current Periodical Reading Room (Serial and Government Publications Division, Library of Congress). Available at: https://www.loc.gov/rr/news/fedgov.html [Accessed September 6, 2022].
– FLOYD HOEFLER