https://en.wikipedia.org/wiki/Australia_(continent)
This is a separate Australia to Australia the Mainland (which doesn't New Guinea), and separate from Australia the country (which includes Tasmania)
Therefore I'm not convinced that "Australia is a continent, so it cannot be an island by definition" rules out the Australia Mainland.
If we look at the wikipedia definition of Island
"subcontinental land completely surrounded by water"
And accept that "Australia the continent" comprises "Australia Mainland", New Guinea (both PNG and part of Indonesia), and nearby islands like Tasmania and Lord Howe (but not New Zealand), then Australia Mainland is surely subcontinental and completely surrounded by water.
Once you leave the English speaking world though, Oceania as a continent comes into play, which goes back to that "definition of continent"