It won’t.

This is how I see ‘giving up a little privacy’ looking. Legitimate/compliant users will link their accounts, the government & Google both enhance their tracking, and the rest of us will abandon our existing accounts (if we have one) and skip out via VPN to a region without this requirement.

MyGovID/DigitalID (maybe as SSO) is my bet; a Google account linked to one of these two government services.

https://my.gov.au/en/about/help/mygov-website/sign-in-to-mygov

https://my.gov.au/en/about/help/digital-id

Whoever wants to compel you for information will add financial/mental/physical pressure until you no longer wish to remain silent. That’s true in democratic governments, stories/history tells us it’s worse in autocratic ones.

You have the right to remain silent… the question is whether you can with external pressure.