The operators of most of those satellites for the US, which I find most people haven't actually heard of:
https://en.wikipedia.org/wiki/National_Geospatial-Intelligen...
Like you mentioned, they do use their capabilities for some things other than just GEOINT:
>In addition to using GEOINT for U.S. military and intelligence efforts, NGA provides assistance during natural and man-made disasters, aids in security planning for major events such as the Olympic Games,[9] disseminates maritime safety information,[10] and gathers data on climate change.[11]
The NRO would be actually the operator. NGA takes care of exploiting the data
Ah shoot, you're right, I totally forgot.
It does make me wonder what the NGA does with a ~5 billion dollar budget then, in my head most it was allocated to new sats. Other than buy approximately 10 3080s I mean ;)
That said, one can correlate the passes of imagery satellites (optical, radar) with other spaceborne RF sensors, and sensors on airplanes & drones (optical, radar, RF etc.), and data from implanted sensors on the ground, to construct a real-time view of the battlespace.
The Full Monty of these capabilities, especially data fusion from disparate platforms, would never be released to the world.
Fun fact: US overhead systems (NRO satellites) are sometimes quietly used to aid search & rescue activities. A friend of mine, a USAF E-9 who had been read into many compartments during his career, used to do this with the Coast Guard after he retired from the Air Force. Pretty cool stuff.