Tweak behavior on Browse screen (#8121)

* Tweak behavior on Browse screen

- Fix system back popping controller
- Add behavior to system back to cancel search toolbar before clearing current search or popping controller

* Review changes

app/src/main/java/eu/kanade/tachiyomi/ui/base/controller/ComposeController.kt

@@ -3,6 +3,7 @@ package eu.kanade.tachiyomi.ui.base.controller
 import android.os.Bundle
 import android.view.LayoutInflater
 import android.view.View
+import androidx.activity.OnBackPressedDispatcherOwner
 import androidx.compose.runtime.Composable
 import eu.kanade.tachiyomi.databinding.ComposeControllerBinding
 import eu.kanade.tachiyomi.util.view.setComposeContent
@@ -24,6 +25,16 @@ abstract class FullComposeController<P : Presenter<*>>(bundle: Bundle? = null) :
             }
         }
     }
+
+    override fun handleBack(): Boolean {
+        val dispatcher = (activity as? OnBackPressedDispatcherOwner)?.onBackPressedDispatcher ?: return false
+        return if (dispatcher.hasEnabledCallbacks()) {
+            dispatcher.onBackPressed()
+            true
+        } else {
+            false
+        }
+    }
 }
 
 /**