The chat button being the only hoverable thing made it feel more like a static image than an actual phone with apps.
If all the apps could be hovered, then presumably you'd be able to click on them too... and that means something would need to happen when clicking them all as well which would be a bunch of unnecessary work.
So, I dunno. Maybe there is another way you can get into the app that is more convincing world building? Like you are actively in some other app, like playing a snake game or something, and it pauses and the AI app notification scrolls in from the top?