Flying from Budapest to Auckland with Air china and will be having a 22h layover in Beijing

If you intend to remain airside (transit area), you do not need to perform any single formality. You do not need to announce anything to anybody and you do not have to fill out any form. Basically, you will just walk from one to the other gate. In the middle you will just cross a typical and usual security check. Also, if you are traveling on a single ticket (entire journey bought at once), you will not collect your luggage, but it will be transferred by airport staff. Also, you will not be a subject of immigration and customs inspections.

I understand that you have written that you do not plan to exit the airport and that is fine, but I just wanted to inform you that you can exit if you want since your layover is a very long one by approaching 24/144 hour visa free transit where you can apply for a temporary entry permit and exit the airport to see the city on your own. Never mind, it will be up to you to decide. Have a nice journey.