While I doubt Google will actually follow through with the threat and completely remove themselves from the Australian market, I can certainly see them tweaking their search algorithms to ensure that they don't bring up Australian news sites.
In fact, Google admitted last week that they are already intermittently blocking some Australian news sites from search users as an a trial. https://www.smh.com.au/politics/federal/google-admits-to-removing-local-news-content-in-experiment-20210113-p56tux.html
This little experiment has meant that for the past couple of weeks I intermittently can't get the Sydney Morning Herald website to come up with a Google search on my home internet. It normally comes up as soon as search SMH. Now, about half the time, it gives me the Herald's Twitter and Facebook pages as top listings and the actual SMH website doesn't appear anywhere on the first three pages of results. Of course it is easy enough just to type in the web address, but who typically does that?
Cutting out the media sites is likely to hurt the media companies more than Google as people will still use the Google search engine for everything else, but with less eyes on their webpages the media companies will start losing subscription dollars and the limited ad revenue that they do have from their sites. Particularly if they themselves have been running Google Ads to backend their online advertising platforms.