Usually I'd search on United'd website, before booking on Aegean, as United has a way better award search.

I have been searching MXP-NAN, found availability on United, but not A3. It includes a flight with Virgin Australia, so I think it makes sense no availability on A3. I change to MXP-SYD, LH + ANA itinerary. Available on UA but not on A3, is this again due to ANA releasing more inventory to UA than to Star Alliance generally?

Thanks!

Edit: I am guessing no, since LH/TG itinerary is also only available on UA and not A3, and as far as I know there are not special agreements outside of Star Alliance between these airlines.