Handle the Back button: close the overlay, then go up, then leave

There was no BackHandler anywhere, so Back was left entirely to the system, which finishes the activity rather than navigating up a folder or closing a viewer. Verified on the phone: Back on the roots screen still exits, and Back inside a folder now goes up and stays in the app.

The handler has to sit above the overlay branch, not after it: that branch returns early, so anything below it is never composed while a viewer or the editor is open, which is precisely when Back most needs an answer. The first attempt made that mistake and the device test caught it.

app/src/main/java/de/softwareapp_hb/filemanager/ui/browser/BrowserScreen.kt

@@ -1,6 +1,7 @@
 package de.softwareapp_hb.filemanager.ui.browser
 
 import android.content.Intent
+import androidx.activity.compose.BackHandler
 import androidx.activity.compose.rememberLauncherForActivityResult
 import androidx.activity.result.contract.ActivityResultContracts
 import androidx.compose.foundation.layout.Box
@@ -133,6 +134,35 @@ fun BrowserScreen(
         state.pendingDeleteRequest?.let { deleteLauncher.launch(it) }
     }
 
+    // Back, in the order a person expects it: close what is on top, then go up a folder,
+    // and only then leave the app. `enabled` is false on the roots screen with nothing
+    // open, which lets the system finish the activity as usual.
+    //
+    // This has to sit *above* the overlay branch below: that branch returns early, so
+    // anything after it is never composed while a viewer or the editor is open — which is
+    // exactly when Back most needs an answer.
+    val closesOverlay = state.overlay != Overlay.None
+    val answersIncoming = state.receiving != null || state.providing || state.pendingDeliver != null
+    val canGoBack = closesOverlay || answersIncoming || searchOpen ||
+        state.query.isNotEmpty() || state.isSelecting || !state.isRootView
+
+    BackHandler(enabled = canGoBack) {
+        when {
+            closesOverlay -> viewModel.closeOverlay()
+
+            answersIncoming -> viewModel.cancelIncoming()
+
+            searchOpen || state.query.isNotEmpty() -> {
+                searchOpen = false
+                viewModel.setQuery("")
+            }
+
+            state.isSelecting -> viewModel.clearSelection()
+
+            else -> viewModel.navigateUp()
+        }
+    }
+
     // A viewer, editor or the usage view takes over the whole screen.
     when (val overlay = state.overlay) {
         is Overlay.Image -> {