Handle mentioned apps via smart context (#1412)

<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Send mentioned apps (names + files) to the engine through
dyad_options, omit inline other-apps prefix when engine is enabled, and
adjust e2e to snapshot request payload.
> 
> - **Engine/Backend**:
> - Pass mentioned apps to engine via
`providerOptions['dyad-engine'].dyadMentionedApps` and forward as
`dyad_options.mentioned_apps` in `llm_engine_provider`.
> - Gate inline other-apps context: only include `otherCodebasePrefix`
when `isEngineEnabled` is false.
> - Enhance `extractMentionedAppsCodebases` to return `files` alongside
`codebaseInfo`.
> - **Tests**:
> - e2e: change `mention app (with pro)` snapshot to
`snapshotServerDump("request")` and update snapshot to assert request
payload contents.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
7ddddf6c16c53cd36b4c7e4ec6a57da0616d1bb0. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

src/ipc/handlers/chat_stream_handlers.ts

@@ -630,18 +630,21 @@ This conversation includes one or more image attachments. When the user uploads
               },
             ] as const);
 
-        const otherCodebasePrefix = otherAppsCodebaseInfo
-          ? ([
-              {
-                role: "user",
-                content: createOtherAppsCodebasePrompt(otherAppsCodebaseInfo),
-              },
-              {
-                role: "assistant",
-                content: "OK.",
-              },
-            ] as const)
-          : [];
+        // If engine is enabled, we will send the other apps codebase info to the engine
+        // and process it with smart context.
+        const otherCodebasePrefix =
+          otherAppsCodebaseInfo && !isEngineEnabled
+            ? ([
+                {
+                  role: "user",
+                  content: createOtherAppsCodebasePrompt(otherAppsCodebaseInfo),
+                },
+                {
+                  role: "assistant",
+                  content: "OK.",
+                },
+              ] as const)
+            : [];
 
         const limitedHistoryChatMessages = limitedMessageHistory.map((msg) => ({
           role: msg.role as "user" | "assistant" | "system",
@@ -720,6 +723,12 @@ This conversation includes one or more image attachments. When the user uploads
             "dyad-engine": {
               dyadRequestId,
               dyadDisableFiles,
+              dyadMentionedApps: mentionedAppsCodebases.map(
+                ({ files, appName }) => ({
+                  appName,
+                  files,
+                }),
+              ),
             },
             "dyad-gateway": getExtraProviderOptions(
               modelClient.builtinProviderId,