this function name doesn't follow our api guidelines:
the name of the composable function which returns unit should start with a capital letter and be a noun. even if it is an extension/member function on other class.
similarly to how we have SaveableStateHolder.SaveableStateProvider()
I don't know what is the best name, maybe Ian would have some ideas. something like:
NavBackStackEntry.LocalOwnersProvider()

Naming is hard :D LocalOwnersProvider isn't that descriptive to me, what do you think of NavBackStackEntry. CompositionLocalProvider? (What Ian originally suggested, just pascal case) @ianhanniballake

(btw, AS keeps telling me that it should indeed start with a lowercase letter😂)

Yeah, I personally liked the scoping of making this an extension on NavBackStackEntry (vs the more obvious top level function of CompositionLocalProvider(NavBackStackEntry, SaveableStateHolder, @Composable () -> Unit)) and yet, the capital lettering feels very odd when it comes to using it with extension functions.

Yeah, I agree - Pascal case extensions are a little weird. I can live with both options but camel case feels more natural to me

I agree that on extension function it looks more strange, but the current guidelines are not having exceptions for extension/member functions.
with LocalOwners I tried to describe what composition locals would be provided, as with just CompositionLocalProvider name it doesn't explain that. but maybe what exactly we provide is an implementation detail, so ok to me

This method would be something that every custom Navigator would use (that's why this needs to be public API).

not blocking this pull-request but just out of my curiosity: what does it mean to have a custom Navigation? if I write my own navigation implementation how will I construct NavBackStackEntry objects?

No, a custom Navigator, not custom Navigation. NavController was built in a such a way that it knows nothing about Fragments, Compose, Views, Dialogs, etc.

It is the individual Navigator instances that are added to the NavController that provide that functionality - ComposeNavigator is just a first party implementation of the public API surface, just like the implementation in #173 is a Navigator specifically designed for modal bottom sheets. They can be mixed and matched and NavController is the one who multiplexes them correctly and controls the creation of NavBackStackEntry instances for each Navigator.