Erm, it might seem that way looking at just the sections of the history that you provided, but a more extensive reading of the Australia section of the Earth/Cyberpunk Sourcebook suggests completely the opposite.
For starters, by 2040 Australia was well on the road to recovery. Then when the Melbourne Accords were signed (putting Australia front and center in probably the most important treaty negotiations in the Earth's history), the UK's refusal to sign paved the way for the very close and incredibly mutually beneficial alliance that Australia shared with the USA thereafter.
An entire arm of human interstellar colonisation was developed by the US-Australia alliance from the late 2160s. Jointly with the US, Australia is effectively a second-tier super-power by 2300.
The independence of Tasmania and a small proportion of Queensland are pretty hilarious. If you have a look at the map of Australia in the Earth/Cyberpunk Sourcebook, the nation of Queensland is just Cape York Peninsula from Cairns northward. How they manage to be a viable nation-state before they annexed Papua New Guinea from the 2260s onwards is beyond me, but that's what canon says so so be it.
Tasmania isn't even viable as a state in real life without massive economic assistance from the rest of Australia, so them becoming an independent nation in T2300 is hilarious. I guess it's some kind of neo-hippy eco-haven or something. Most Australians wouldn't give two stuffs if Tasmania declared independence (no doubt Legbreaker will have something to say about that
).
In any case, Oceania in 2300 seems to have something like an EU arrangement going on, so Australia, New Zealand, "Papua", "Tasmania" and the South Pacific island states would be closely economically interconnected and interdependent anyway. To do otherwise would be pretty stupid for the non-Australian nations of Oceania.
So all in all, I'd say that "It seems Australia didn't do that well after all" is a reasonable statement regarding Australia during and immediately after the Twilight War, but is completely refutable in the longer term.