fix(nav): keep Home below tab roots, hide back arrow via per-entry flag

Previous attempt cleared Home from the back stack on every bottom-nav
tap, which broke back-swipe: the user expects swipe-back from any tab
to return to Home, and swipe-back from Home to leave the app.

Restore that contract while still hiding the back arrow on tab roots:
- navBottomBar pops up to (but not including) Route.Home, so sibling
  tabs are cleared while Home stays at the bottom of the stack.
- The new entry is stamped with BOTTOM_NAV_ROOT_KEY on its
  savedStateHandle.
- Nav.canPop returns false when the current entry carries that flag,
  even though previousBackStackEntry (Home) is non-null.

Home itself is the graph's start destination and has no previous entry,
so canPop returns false there without needing the flag.

https://claude.ai/code/session_01PrirRcL7g8iX7vTqqLTkBS

amethyst/src/main/java/com/vitorpamplona/amethyst/ui/navigation/NavigationEffects.kt

@@ -41,6 +41,13 @@ const val SKIP_SLIDE_ANIMATION_KEY = "skipSlideAnimation"
 
 fun NavBackStackEntry.skipsSlideAnimation(): Boolean = savedStateHandle.get<Boolean>(SKIP_SLIDE_ANIMATION_KEY) == true
 
+// Per-entry hint stamped by Nav.navBottomBar marking that the entry was
+// reached via a bottom-nav tab. Used by Nav.canPop so top bars can hide
+// the back arrow on tab roots even though Home sits below them.
+const val BOTTOM_NAV_ROOT_KEY = "bottomNavRoot"
+
+fun NavBackStackEntry.isBottomNavRoot(): Boolean = savedStateHandle.get<Boolean>(BOTTOM_NAV_ROOT_KEY) == true
+
 inline fun <reified T : Any> NavGraphBuilder.composableFromEnd(noinline content: @Composable AnimatedContentScope.(NavBackStackEntry) -> Unit) {
     composable<T>(
         enterTransition = { if (targetState.skipsSlideAnimation()) null else slideInHorizontallyFromEnd },

amethyst/src/main/java/com/vitorpamplona/amethyst/ui/navigation/navs/Nav.kt

@@ -24,9 +24,10 @@ import android.annotation.SuppressLint
 import androidx.compose.material3.DrawerState
 import androidx.compose.material3.DrawerValue
 import androidx.compose.runtime.Stable
-import androidx.navigation.NavGraph.Companion.findStartDestination
 import androidx.navigation.NavHostController
+import com.vitorpamplona.amethyst.ui.navigation.BOTTOM_NAV_ROOT_KEY
 import com.vitorpamplona.amethyst.ui.navigation.SKIP_SLIDE_ANIMATION_KEY
+import com.vitorpamplona.amethyst.ui.navigation.isBottomNavRoot
 import com.vitorpamplona.amethyst.ui.navigation.routes.Route
 import com.vitorpamplona.amethyst.ui.navigation.routes.getRouteWithArguments
 import kotlinx.coroutines.CoroutineScope
@@ -79,22 +80,28 @@ class Nav(
     override fun navBottomBar(route: Route) {
         navigationScope.launch {
             controller.navigate(route) {
-                // Clear the back stack down to and including the graph's start
-                // destination so a bottom-nav tap leaves only the new route in
-                // the stack. Without inclusive=true, Home would remain below
-                // the new tab and canPop() would wrongly show a back arrow.
-                popUpTo(controller.graph.findStartDestination().id) {
-                    inclusive = true
+                // Clear sibling bottom-nav entries but keep Home (the start
+                // destination) below, so back-swipe from any tab returns to
+                // Home and back-swipe from Home leaves the app.
+                popUpTo(Route.Home) {
+                    inclusive = false
                 }
                 launchSingleTop = true
             }
-            // Stamp the entry so composableFromEnd's transition lambdas can
-            // skip the slide animation when this entry enters or exits.
-            controller.getBackStackEntry(route).savedStateHandle[SKIP_SLIDE_ANIMATION_KEY] = true
+            val entry = controller.getBackStackEntry(route)
+            // Skip the horizontal slide for composableFromEnd transitions.
+            entry.savedStateHandle[SKIP_SLIDE_ANIMATION_KEY] = true
+            // Mark this entry as a tab root so canPop hides the back arrow
+            // even though Home sits below it.
+            entry.savedStateHandle[BOTTOM_NAV_ROOT_KEY] = true
         }
     }
 
-    override fun canPop(): Boolean = controller.previousBackStackEntry != null
+    override fun canPop(): Boolean {
+        val current = controller.currentBackStackEntry ?: return false
+        if (current.isBottomNavRoot()) return false
+        return controller.previousBackStackEntry != null
+    }
 
     override fun popBack() {
         navigationScope.launch {