Delete DuckChatWebViewActivity (#7328)

Task/Issue URL:
https://app.asana.com/1/137249556945/project/488551667048375/task/1211755763011422?focus=true

### Description

- This is no longer needed since Duck.ai is currently tied to the
`BrowserActivity` using `DuckChatWebViewFragment`

### Steps to test this PR

- [ ] Open Duck.ai
- [ ] Verify that it is launched correctly

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> Deletes the standalone DuckChatWebViewActivity and shifts
opening/closing Duck.ai to BrowserNav with updated session handling;
cleans up manifest and tests.
> 
> - **DuckChat flow**:
> - Remove `DuckChatWebViewActivity` and
`DuckChatWebViewActivityViewModel` (and related tests).
> - In `RealDuckChat`, drop `keepSession` and standalone activity path;
always use `BrowserNav.openDuckChat/closeDuckChat`.
> - Adjust session logic: `hasSessionActive` now based on
`hasActiveSession()` unless `forceNewSession`.
> - Remove `DuckChatWebViewActivityWithParams` usage and
`startDuckChatActivity` helper.
> - **Manifest**:
> - Delete `com.duckduckgo.duckchat.impl.ui.DuckChatWebViewActivity`
entry.
> - **Tests**:
> - Update `RealDuckChatTest` to assert `BrowserNav` intents and
active-session behavior; remove obsolete WebView activity tests.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
6957e7a. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Author: joshliebe

duckchat/duckchat-impl/src/main/AndroidManifest.xml

@@ -27,11 +27,6 @@
             android:exported="false"
             android:label="@string/duck_ai_shortcut_settings_title"
             android:parentActivityName="com.duckduckgo.duckchat.impl.ui.settings.DuckChatSettingsActivity" />
-        <activity
-            android:name="com.duckduckgo.duckchat.impl.ui.DuckChatWebViewActivity"
-            android:exported="false"
-            android:label="@string/duck_chat_title"
-            android:configChanges="keyboardHidden|orientation|screenSize|smallestScreenSize|screenLayout|navigation|keyboard"/>
         <activity
             android:name="com.duckduckgo.duckchat.impl.inputscreen.ui.InputScreenActivity"
             android:exported="false" />

duckchat/duckchat-impl/src/main/java/com/duckduckgo/duckchat/impl/RealDuckChat.kt

@@ -49,7 +49,6 @@ import com.duckduckgo.duckchat.impl.pixel.DuckChatPixelName.DUCK_CHAT_NEW_ADDRES
 import com.duckduckgo.duckchat.impl.pixel.DuckChatPixelParameters
 import com.duckduckgo.duckchat.impl.pixel.DuckChatPixelParameters.NEW_ADDRESS_BAR_SELECTION
 import com.duckduckgo.duckchat.impl.repository.DuckChatFeatureRepository
-import com.duckduckgo.duckchat.impl.ui.DuckChatWebViewActivityWithParams
 import com.duckduckgo.navigation.api.GlobalActivityStarter
 import com.duckduckgo.privacy.config.api.PrivacyConfigCallbackPlugin
 import com.squareup.anvil.annotations.ContributesBinding
@@ -297,7 +296,6 @@ class RealDuckChat @Inject constructor(
     private val _showMainButtonsInInputScreen = MutableStateFlow(false)
 
     private val _chatState = MutableStateFlow(ChatState.HIDE)
-    private val keepSession = MutableStateFlow(false)
     private val _showInputScreenOnSystemSearchLaunch = MutableStateFlow(false)
     private val _showVoiceSearchToggle = MutableStateFlow(false)
     private val _showFullScreenMode = MutableStateFlow(false)
@@ -410,15 +408,9 @@ class RealDuckChat @Inject constructor(
     }
 
     override fun closeDuckChat() {
-        if (keepSession.value) {
-            browserNav.closeDuckChat(context).apply {
-                flags = Intent.FLAG_ACTIVITY_NEW_TASK
-                context.startActivity(this)
-            }
-        } else {
-            appCoroutineScope.launch {
-                closeChatFlow.emit(Unit)
-            }
+        browserNav.closeDuckChat(context).apply {
+            flags = Intent.FLAG_ACTIVITY_NEW_TASK
+            context.startActivity(this)
         }
     }
 
@@ -552,21 +544,15 @@ class RealDuckChat @Inject constructor(
             val hasSessionActive =
                 when {
                     forceNewSession -> false
-                    keepSession.value -> hasActiveSession()
-                    else -> false
+                    else -> hasActiveSession()
                 }
 
             duckChatFeatureRepository.registerOpened()
 
             withContext(dispatchers.main()) {
                 pixel.fire(DuckChatPixelName.DUCK_CHAT_OPEN, parameters = params)
-                if (keepSession.value) {
-                    logcat { "Duck.ai: restoring Duck.ai session $url hasSessionActive $hasSessionActive" }
-                    openDuckChatSession(url, hasSessionActive)
-                } else {
-                    logcat { "Duck.ai: opening standalone Duck.ai screen $url" }
-                    startDuckChatActivity(url)
-                }
+                logcat { "Duck.ai: restoring Duck.ai session $url hasSessionActive $hasSessionActive" }
+                openDuckChatSession(url, hasSessionActive)
             }
         }
     }
@@ -584,16 +570,6 @@ class RealDuckChat @Inject constructor(
                 context.startActivity(this)
             }
     }
-
-    private fun startDuckChatActivity(url: String) {
-        globalActivityStarter
-            .startIntent(context, DuckChatWebViewActivityWithParams(url))
-            ?.apply {
-                flags = Intent.FLAG_ACTIVITY_NEW_TASK
-                context.startActivity(this)
-            }
-    }
-
     private fun appendParameters(
         parameters: Map<String, String>,
         url: String,
@@ -721,7 +697,6 @@ class RealDuckChat @Inject constructor(
             isImageUploadEnabled = imageUploadFeature.self().isEnabled()
             isStandaloneMigrationEnabled = duckChatFeature.standaloneMigration().isEnabled()
 
-            keepSession.value = duckChatFeature.keepSession().isEnabled()
             keepSessionAliveInMinutes = settingsJson?.sessionTimeoutMinutes ?: DEFAULT_SESSION_ALIVE
 
             cacheUserSettings()