AloofChocolate
I did, formally, about a year ago.
The email address listed for the App actually bounced. So I persisted, and contacted Services Australia direct, requesting and eventually (thanks to a helpful person) being provided a working method of submitting feedback concerning the app.
Subsequently, updates of the app have mostly addressed additional features (once logged in) and usability concerns. All that has changed since (relevant to ability or otherwise of logging in if the MyGov App is installed on GOS) is that, instead of getting a cryptic error message after successfully logging in, the App now prevents access to login screens.
As a result, I clearly don't bother with the App. When I need to login to MyGov services (ATO, Medicare, etc) I use a browser on a desktop PC. That works quite well, with either Windows 11 or Manjaro operating systems.