[SB][ComposeIcons] Replace legacy status icons in the UI

Previously, the composable icons were added towards the
center of the screen and the existing icons were kept visible.
The icons are close to ready for staging now so this CL replaces
the `statusIcons` view with the new composable.

Bug: 406922954
Test: Manual, Screenshot test TBA.
Flag: com.android.systemui.status_bar_system_status_icons_in_compose
Change-Id: I3ec7fcafb7856940dddf04b579e0102c0dce7bb0