Hide keyboard in unfocussed state when Input Screen enabled (#6862)

Task/Issue URL:
https://app.asana.com/1/137249556945/project/488551667048375/task/1211370636939092?focus=true

### Description

- Hides the keyboard in the unfocussed state when the Input Screen is
enabled.

### Steps to test this PR

_Input Screen enabled_
- [x] Create a new tab and go to a web page
- [x] Go back
- [x] Verify that the keyboard is not shown

_Input Screen disabled_
- [x] Create a new tab and go to a web page
- [x] Go back
- [x] Verify that the keyboard is shown and the omnibar is focussed

Author: joshliebe

app/src/androidTest/java/com/duckduckgo/app/browser/BrowserTabViewModelTest.kt

@@ -2632,6 +2632,16 @@ class BrowserTabViewModelTest {
         assertTrue(commandCaptor.allValues.contains(Command.ShowKeyboard))
     }
 
+    @Test
+    fun whenUserPressesBackAndGoesToHomeWithInputScreenEnabledThenKeyboardNotShown() {
+        whenever(mockDuckAiFeatureState.showInputScreen).thenReturn(MutableStateFlow(true))
+
+        setupNavigation(isBrowsing = true, canGoBack = false, skipHome = false)
+        testee.onUserPressedBack()
+
+        assertCommandNotIssued<ShowKeyboard>()
+    }
+
     @Test
     fun whenUserPressesBackOnATabWithASourceTabThenDeleteCurrentAndSelectSource() =
         runTest {

app/src/main/java/com/duckduckgo/app/browser/BrowserTabViewModel.kt

@@ -1429,7 +1429,9 @@ class BrowserTabViewModel @Inject constructor(
             }
             return true
         } else if (!skipHome && !isCustomTab) {
-            command.value = ShowKeyboard
+            if (!duckAiFeatureState.showInputScreen.value) {
+                command.value = ShowKeyboard
+            }
             navigateHome()
             return true
         }