I’m aware you are knowledgeable but why would you assert that stealth design principles do not work in space? (Not referring to the x37 here but generally).
Long version: “Stealth” involving radar absorption causes the craft to heat up. This means you can see it more clearly on infrared/thermal. You can see the vessel with a camera array, as it will block out background stars or other light sources. If the vessel uses any sort of thruster to move at all, the ejecta will be observed.
Using commercial technology of the time, the Space Shuttle firing an attitude control jet could be detected out past the solar system’s asteroid belt. Transmission by radio or using an ion thruster is even worse - it takes less than one second for a private radiotelescope to see a 20 watt source out past 18 *billion* km. Which is exactly how we locate and talk to the Voyager space probes.
There is no horizon to hide over, no ground clutter to disappear in. You can’t even hide in the sun.
More reading: http://www.projectrho.com/public_html/rocket/spacewardetect.php