A family of Microsoft word processing software products for creating web, email, and print documents.
The info & options offered in Page Setup are provided by the driver software for the printer drivers you have installed -- they are not provided by Word. If A3 isn't in the list it's because the selected printer doesn't have the capacity to print on that size stock. Try choosing Any Printer from the Format For: list & see if A3 [along with a number of others you hadn't seen] shows up.
It sounds like you're aware that you can specify any dimensions you wish by using the Manage Custom Sizes feature to define the paper sizes you prefer... That, however is an OS X feature -- again, simply hosted by the program you're using.
IOW, everything in Page Setup is basically Word saying "OK, this is what I've been given for you to pick from."