It's widely accepted in the commercial two way satellite telecom industry that the NSA has comparable things with big unfolding umbrella-like antennas in geostationary which serve a similar purpose for signals collection.
How does that even work, do people just accept that their satellites hang around suspiciously close to other geostationary satellites and hoover up the very edge of the beam somehow?
Because if you're transmitting stuff *to* geosynchronous birds you have to aim pretty accurately.
If you have a NSA-type geostationary satellite somewhere in approximately a 1/5th arc of azimuth along the equator of the earth that can 'see' an area on the ground, with antenna systems aimed at the area of interest (let's say, Afghanistan), it's not necessary for your NSA satellite to be anywhere close to the actual service provider's satellite.
Note that Thuraya BGAN-like devices and handheld phones talk to geostationary, Iridium is LEO (but likely some combination of LEO, molniya orbit and geostationary can "sniff" it), Globalstar is similarly LEO in its service provider architecture, and Inmarsat is geostationary.
Also lots of conjecture out there that sigint platforms exist which are good enough to capture ordinary handheld device cellular traffic or VHF/UHF radio traffic that's not intended by its users or terrestrial operators to go into space at all. This is probably done from a combination of low earth orbit platforms and more complicated orbits or what we would call MEO (maybe about the same height as an o3b satellite?) to achieve longer dwell times over an area of interest.
Same concept for an Iridium 9555 or its successor in a dock plugged into the small coaxial cable that goes to the external hockey puck sized antenna. This is all happening between approx. 1400 to 1700 MHz in either system.
Look up the detailed RF specs for the isatphone 2.
Both of these only work because the channel size is extremely narrow.
The antenna on the commercial satellites that do two way S/L-band to handheld stuff (or INMARSAT BGAN size terminals) from geostationary is massive, I've no reason to believe that a high budget billion dollar NSA satellite at MEO or higher altitudes wouldn't have a similarly gargantuan unfolding antenna.
Nobody does what you are saying, because physics, which leads me to believe that you are confused.
https://en.wikipedia.org/wiki/USA-202