Android has historically allowed third-party app stores to be installed as well as sideload individual APKs but the process of doing so is not very streamlined and there’s no way to update sideloaded apps automatically.
This would change with Android 12, according to Google’s own blogpost. XDA-Developers dug deeper into the source code and goes into details of what those changes would be like.
The new system will allow third-party app stores not only to install apps directly but also update them in batches automatically. Of course, the user still has to grant the app store’s permission to manage internal storage. But it would be one-time permission and won’t ask again in the future. Just like the default Google Play Store.