I'd like to use BottomNavigation where each tab remembers its navigation state. Is this supported with Compose Navigation?

Idk about implementation in Compose Navigation but you can definitely build a system on top of Current Jetpack Navigation. Here's a reference implementation: https://github.com/chrisbanes/tivi/blob/main/common-ui-view/src/main/java/app/tivi/extensions/MultipleBackStackNavigationExtensions.kt

Multiple back stacks, when implemented, will be supported in both a fragment based Navigation and Compose based

@Ian Lake Is there any plan to have a single lifecycle for fragment and it's view?