Given the USSR also built the Tu-144 so you're probably right about it being a case of envy, though the shuttle is fairly unique in that it can retrieve things from space and bring them back, something not practical in a Soyuz or Dragon-type vehicle.
I can imagine if the military had orbit-capable telescopes like those sitting around, there must be many ground-based ones used to track other satellites.
Retrieving satelites never really held water.
Your own payloads would have to be very very valuable to be worth the cost and risk of manned launch and rendezvous and the shuttle couldn't land with something the mass of HST or a KH spy sat
Snatching an enemy's property is even more risky - as soon as the opposition has the capability you would fit your special toys with an anti-handling device. I don't work on the 'dark side' but I'm betting that anything special has a self destruct anyway just in case a launch goes wrong and it is retrieved.
You could even launch a whole constellation consisting of just a proximity fuse, a few kg of C4 and some ball bearings and wait for the other side to go fishing in their $billion space plane.
There was a very large US program to send up a photo sat manned, take pictures, and send back to earth in very small pods. It is a good read I will update post if I can find video.
I was only involved in Hubble after it was built, but my boss had conference proceedings from the early 70s were it was proposed that it would be a Skylab type space station with a crew of 3 loading photographic plates into a telescope and then developing them!
A return was considered in place of the COSTAR servicing mission, I can't remember if there was a 'safety margin' in that figure or there was another reason - but it was rejected for safety reason.
I can imagine if the military had orbit-capable telescopes like those sitting around, there must be many ground-based ones used to track other satellites.