Exactly. It's actually easy to find spies in any country, even the US. They are all embassy employees, no joke. This is how it has always been.

With the USSR you just had to look at the Soviet embassy in Washington DC and consulates in the rest of the US. The actual counter espionage, done by the FBI and not US Congress persons, involved following embassy employees around to monitor who they interacted with. The FBI and KGB agents ended up having what one would describe as a professional relationship knowing each other by name. The situation was the same in the USSR but with roles reversed.

For the US spying, the CIA station chief for an area is also a senior embassy employee with a sizeable percentage of US embassy staff also being CIA agents, everyone who is a regular state dept embassy employee knows which of their coworkers are CIA and everyone just doesn't talk about it. This is still the case today, I suggest looking up details the Chinese government has released when they have to arrest then debrief some of their own citizens who got suckered in by US embassy employees who made friends with them in their personal life but were CIA agents that began blackmailing them to do things.

Remember the Hillary Clinton comedy involving the US consulate in Benghazi that became a shit show because EVE-ONLINE mmorpg players kept writing the media and congress people over not understanding their dead gamer buddy wasn't some innocent US State Dept employee but was a CIA agent running guns out of a US consulate in Libya?