Not America...
《However, for as long as Twitter wants to have a presence in Australia, the government can make that conditional on anything it likes, within the bounds of whatever the constitution permits.》
The AU constitution is very different creature quite unlike that of the US. Not carte blanche to slaughter your fellow citizen with the firearm of your choice, or even a bill of rights.
It largely deals with the separation of powers, relations between the various governments and structure of the federal legislature and judiciary.
It suspect it would impose very few constraints on the Commonwealth's ability to legislate in this area. Using section 92 to object would be drawing a rather long bow, nailing legs onto a dead horse.
Musk's antics are likely to lose what few remaining Australian twitter users that are still within cooee of sanity.
In any case after this Australian institutions will start closing their twitter accounts and removing their presence.
Australians are a bit odd in that unlike their american cousins they would prefer their local news footage to have as little similarity to the comparable US material which ressembles nothing so much as an endless stream of snuff movies.
I would imagine the Commonwealth already has powers to compel network providers to block traffic from any source. Many states still have Victorian era obscenity and public decency laws on their books which could be dusted off and revived.