There is a widely accepted difference between islands and continents in terms of geology. Continents are often considered to be the largest landmass of a particular continental plate; this holds true for Australia, which sits on its own continental lithosphere and tectonic plate (the Australian Plate).
By contrast, islands are usually seen as being extensions of the oceanic crust (e.g. volcanic islands), or as belonging to a continental plate containing a larger landmass (continental islands); the latter is the case of Greenland, which sits on the North American Plate.
There's no clear definition and there's far to much political and cultural meaning in the definition of a continent so any definition involving the term is going to be ambiguous.
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"