So several problems with infrastructure - the developers always underquote and then once there are overruns the government is locked in and doesn't want to bankrupt the companies making these public infrastructure projects otherwise nobody would ever build anything. Additionally borrowing for infrastructure is often done through public/private partnerships which ends up with private companies owning the infrastructure and payments being made by the government for all sort of things in addition to rent i.e. changing a lightbulb costs £2000 etc. Government tend to get all the downside and the rich (who own the debt and the companies involved in building these projects) tend to see all the upside, look at the utility and train companies in the UK for example, and hospitals under PFI.
The money for these projects is provided by the wealthy through the purchase of government bonds.
Brexit is a problem sure, nobody denies that, but QE of around £1tn since COVID, most of which ended up with the richest (see asset price increases and cash holdings and world stock markets at all time record levels) is even more of a problem as it makes normal people and tax income relatively even smaller so borrowing and taxes need to be increased. And of course we don't tax the people whose assets have gone up enormously until they sell those assets. Quite often rich people borrow money against those assets instead of realising a capital gains tax event or various other loopholes.
I don't know too much about the specific case of transport infrastructure in Australia, but if the government owned them outright without attached debts clearly they would be assets rather than liabilities.