The purpose of the social media law is to prevent people under 16 from from being able to post online (they’re allowed to read).
Age verification for app stores including the Steam store, adult media etc is only slightly related to the under 16 social media restrictions on the interactive side. The social media rules were rushed through in a moral panic but all the other restrictions have been in the works for a long time and there has been a lot of industry discussion.
The reported aim is to bring online 18+ content into line with the physical world where a minor can't walk into a brothel, adult shop or casino or buy alcohol or tobacco. Obviously quite a lot of us think there is a secondary objective of de-anonymizing Internet use for data collection, both corporate and government.
The scope and ambition of the esafety commisioner is very broad. There are discussions down to the level of operating systems, devices and browsers.