Don't connect the SSE API when running embedded (#9020)

See #8298
See #8763

Author: DanTup

packages/devtools_app/lib/src/shared/config_specific/framework_initialize/_framework_initialize_web.dart

@@ -28,12 +28,15 @@ Future<String> initializePlatform() async {
       );
 
   // TODO(kenz): this server connection initialized listeners that are never
-  // disposed, so this is likely leaking resources.
+  //  disposed, so this is likely leaking resources.
   // Here, we try and initialize the connection between the DevTools web app and
   // its local server. DevTools can be launched without the server however, so
   // establishing this connection is a best-effort.
-  // TODO(kenz): investigate it we can remove the DevToolsServerConnection
-  // code in general. We do not appear to be using the SSE connection.
+  // TODO(kenz): investigate if we can remove the DevToolsServerConnection
+  //  code in general - it is currently only used for non-embedded pages to
+  //  support some functionality like having VS Code reuse existing browser tabs
+  //  and showing notifications if you try to launch when you already have one
+  //  open.
   final connection = await DevToolsServerConnection.connect();
   if (connection != null) {
     setGlobal(Storage, server.ServerConnectionStorage());

packages/devtools_app/lib/src/shared/server/server_api_client.dart

@@ -5,6 +5,7 @@
 import 'dart:async';
 import 'dart:convert';
 
+import 'package:devtools_app_shared/ui.dart' show isEmbedded;
 import 'package:devtools_shared/devtools_shared.dart';
 import 'package:flutter/foundation.dart';
 import 'package:http/http.dart' as http;
@@ -47,6 +48,14 @@ class DevToolsServerConnection {
           : baseUri.resolve('api/');
 
   static Future<DevToolsServerConnection?> connect() async {
+    // Don't connect SSE when running embedded because the API does not provide
+    // anything that is used when embedded but it ties up one of the limited
+    // number of connections to the server.
+    // https://github.com/flutter/devtools/issues/8298
+    if (isEmbedded()) {
+      return null;
+    }
+
     final serverUri = Uri.parse(devToolsServerUriAsString);
     final apiUri = apiUriFor(serverUri);
     final pingUri = apiUri.resolve('ping');