I think the Watch is a better precedent than the Apple TV. The product page already borrows its vocabulary: customizable faces, Live Activities, and “compatible third-party audio and video apps from your iPhone.” That’s how WatchKit started in 2015. Third-party Watch apps ran as extensions on the paired iPhone, went native with watchOS 2 later that year, and didn’t get an on-device App Store until watchOS 6 in 2019.

So I wouldn’t expect a HomeView App Store soon. I’d expect iPhone-hosted extensions first (widgets, Live Activities, CarPlay-style templates for audio and video), probably at WWDC. That also spares developers who are already scrambling to support the Duo.