So Morrison has no power, no budget, no army, etc. If he is that powerless, why bother being PM?
I posted a long post trying to explain some of this the other day.
So what is going on in Australia? View from an Australian Freeper
But, in brief, to try and answer your questions.
The Prime Minister does have real power but only in areas the Commonwealth government (Australia's Federal level government) has specifically and explicitly been given power over in Section 51 of Australia's Constitution. Section 51 is actually basically a simple list of all the areas controlled by the Commonwealth government. The Commonwealth government has absolutely no power over any area not mentioned in Section 51.
The states (they were called colonies then) wrote the Constitution and deliberately kept hold of a lot of areas for themselves.
And one of those is 'public health'. The Prime Minister, and the Commonwealth government cannot overrule a state government on any matter relating to public health. That has left the state governments in control of the pandemic response, and the Commonwealth government has had to accept that.
The Prime Minister and his government does have power over the Federal budget, but it's dispersal to the states is managed by agreements negotiated over time. The Prime Minister cannot alter those agreements unilaterally so he can't just deny money to states to try and exert control.
Likewise, while defence is a Commonwealth power, the Constitution explicitly does not allow the government to use the military to try and overrule state laws, even if a government wanted to be that tyrannical.
Foreign affairs, international trade, defence... there's plenty of areas the Commonwealth government does have power over.
But in their domains, the individual state governments are more powerful than the Commonwealth government by deliberate design.