Looks like NSW doesn't allow ICE motorised bicycles now,
only electrics.
Vic still does, but only <200W engines.
The recent [last 10 years or so] changes to the road rules were pretty much triggered by the advent of the Asian made 'monkey bikes', some of which were up to ~2/3 scale road bike replicas with 50cc engines.
But they were nowhere near ADR compliant [therefore not able to be registered here], and had all sorts of safety/quality issues [brakes, throttles, footpegs, steering, no kill switches...]. That got them banned from sale [though there are still importers that try it], as well as the road rules changes.
Before the rules changed, I used to see a couple of these things being ridden around the streets in Sale, Vic by eejits with no road sense; every time, I just had to shake my head and think that the sooner they were put off the road, the better. That's from the perspective of a '30+ year licensed' motorcyclist...
Some States [QLD, WA, NT and SA] permit ADR-compliant LA-class 50cc scooters [i.e. no pedals] to be ridden on a car licence now, but the scooter still needs to be registered/third party cover insured.