Finding and tracking objects beyond GEO
Tracking far away satellites involves a unique set of challenges. Predominantly it is a test of detection sensitivity as the farther away an object is, the fainter it will appear. However, because the objects are moving we cannot simply increase the exposure time to detect fainter objects. The effective exposure time is limited to the time it takes for the target object to cross the detector pixels. If we have accurate ephemeris information, we can track the object and increase the exposure time and overall sensitivity. However, for objects beyond GEO, available ephemeris is often poorly accurate or not available at all. Tracking these objects requires first finding them, and then attempting to match their motion.
Interestingly, once an object is far enough away (e.g. JWST), the apparent motion is slow enough that there is no difference in maximum exposure time, and therefore sensitivity, between sidereal tracking and tracking the object. Thus there is a region between approximately GEO and lunar distance where tracking is difficult because there is not readily available ephemeris (too far away) and the apparent motion is too high for sidereal tracking (not far away enough).
Specifically for cislunar space in the vicinity of a bright Moon, the sky background brightness is a significant a limiting factor. In this scenario, longer exposure times are not possible because the sky background will saturate the detector before a meaningful detection is possible. Similarly, larger aperture telescopes do not necesarily improve sensitivity. Tracking objects against a bright sky requires entirely different observing methodology using shorter exposure time and minimizing stray light.