I don't think the ATO has such a list. They do maintain a list of payroll software but it's ridiculously long (MYOB alone has dozens of entries) and I suspect it's not a complete either.
https://softwaredevelopers.ato.gov.au/product-register
They don't list wether any of it runs on linux, or which ones even work at all... and in particular if you have employees then you need to be careful as calculating the wrong amount of pay (or superannuation) could be classified as wage theft, and you can go to jail for that.
If you're just doing your own tax, then it's a lot easier and the penalty for an honest mistake is reasonable (often no penalty at all...). You could just do it all on paper without any issues, or an openoffice spreadsheet, or free/open source software like ledger-cli.org.