Having the Government run ~200 stores isn’t going to drastically cut prices to make things more affordable, not without underpaying staff or suppliers?
As a government-run business, they have no need to pursue profit; they provide a service to people. The point of state-run grocery stores is to spend government money providing for people's needs, there is no justification to underpay workers nor suppliers, nor to overcharge for the groceries.
Pay the suppliers a fair rate for their goods; this might be above what the duopolists pay, and that's no problem. Charge a retail price low enough that people can afford groceries. Pay the workers enough to decently remunerate their work; this might be above what other grocery workers are paid, and that's no problem.
The Australian government can always pay whatever Australian dollars are needed for this. By legislating they will pay the money they thereby create the money to pay for it. We should demand they pay for whatever is needed to provide what we need, without any condition on the business to return any profit.
Perhaps that results in a business that returns no profit. Perhaps as a business even ends up spending more money than it brings in. This is fine, so long as it does what we need it to do for that money spent.
(For those concerned with the risk of inflation by spending government money: that's a valid concern! But paying decent prices to farmers for food, paying decent wages to workers in the grocery stores, is not what drives inflation. Let's reduce inflation by taxing away the super-wealth of billionaires.)
All of these valid goals are compatible simultaneously, because there is no need for the state-run grocery business to be profitable. Government is meant to provide for its people, it is irrelevant whether the business returns a profit.