Whenever I hear about this I can't help but be reminded of the Howard Hughes Glomar Explorer, where a hugely-expensive commercial project was actually part of a secret CIA initiative to recover a Soviet submarine: https://en.wikipedia.org/wiki/Glomar_Explorer
I'm not sure that's truly the case here, but it does seem like the tech Project Suncatcher is working on has at least some overlap with requirements for military SIGINT and in-orbit imagery processing.
Why would the CIA need Google's cover for any of that? The Feds have been flying spy satellites since the 1950s and there's plenty of classified satellite launches.