A quick list of the canonical resources. You really won’t need anything else other than these.
This is an astrophysics olympiad after all, so you'll need a good physics background. For that, check out Kevin Zhou’s handouts and advice. You can also check out my website :)
USAAAO guide - a very well-written set of notes, kind of the equivalent of Kevin Zhou’s handouts but for astronomy.
AO Guide - a relatively new resource for learning astronomy. includes a small number of practice problems.
Stellar Guesser - a really good app that allows you to test your knowledge of practical astro
I don’t find textbooks to be very helpful due to their sheer length, but you may find them useful if you are new to astronomy.
Fundamental Astronomy by Karttunen - a concise introduction to astronomy
An Introduction to Modern Astrophysics by Caroll & Ostlie - a longer book, but very thorough.
Astronomy competitions are often littered with mistakes. You can find a list of errors on Stefan Ivanov's website. Most competitions listed here can be found in Stefan Ivanov's archive. Alternatively, you can check out AstroSandbox.
IOAA - classic. can often be straightforward but very long, kind of similar to ipho.
USAAAO - an interesting olympiad with many challenging problems. rarely has errors from 2019 onwards, but you can check out the errata list.
Czech Astronomy Olympiad - a very good olympiad that rarely has errors.
Singapore Astronomy Olympiad - occasionally has interesting problems. difficulty and quality can be on many different orders of magnitude. has a ton of errors.
Russian Open World Astronomy Olympiad - a really old competition that only ran for 4 years. This is one of the few places you can find short and tricky problems you sometimes see in physics competitions like EuPhO and NBPhO.
That’s really all you need! If you want to learn practical astronomy such as constellations and DSOs, check out Stellarium and Turn Left at Orion (a book).