Non-native speaker here.

I always assumed Fed has something to do with FBI or the Federal Bank. Please, can someone explain me what Fed means in this context?

Thank you in advance

In the context of my childhood, feds were everywhere:

From the founder of Costco, FedMart was a department store chain and the predecessor to Target

Federal Express Corporation was founded in the early 1970s and, of course, shortened up their name. Don't miss the arrow in their logo!

There were some consumer electronics stores named "Federated" and their commercials featured a mascot named "Fred Rated"

Institutions such as banks sometimes took names like "First Federal" which could give an impression of being a government agency, but probably referred to their organizational structure or nationwide presence. Different from the Federal Reserve and the Federal Reserve Banks.

Yes, based on context fro. a quick skim of the content, it sounds like its a jokey reference to working the FBI phone switchboard