It seems to me that a lunar synchronous orbit would actually be not only around the moon, but around the Earth-moon system and be a real headache to maintain, but maybe not.
Putting space observatories out in very distant Lagrange points is something NASA is pretty good at (Solar observatories, etc). I don’t know of anyone using the L2 point behind the moon, and besides the great distance, you may need a relay to see it since its at least partially masked by the moon. I don’t think the Chicoms have gotten to where they support the required infrastructure yet, but I haven’t kept up. Maybe they have.
Both a high single platform, or a low constellation, are challenging but doable, if you have enough resources.