[cleanup][sdk] refactor usages of connectToEnvironmentService

MS-2335 #comment

Test:
1. compiles
2. CQ
3. run mind_reader

Change-Id: I8482a939df5f7e8232a162c738efb269799566f2
diff --git a/public/dart/fuchsia_services/examples/mind_reader/bin/server/lib/src/_mind_reader_impl.dart b/public/dart/fuchsia_services/examples/mind_reader/bin/server/lib/src/_mind_reader_impl.dart
index c630d1d..334fa76 100644
--- a/public/dart/fuchsia_services/examples/mind_reader/bin/server/lib/src/_mind_reader_impl.dart
+++ b/public/dart/fuchsia_services/examples/mind_reader/bin/server/lib/src/_mind_reader_impl.dart
@@ -32,7 +32,9 @@
     // succeed the service must have been explicity exposed to us by the parent
     // process and we must identify that we can connect to it in our component
     // manifest file.
-    connectToEnvironmentService<ThoughtLeaker>(proxy);
+    StartupContext.fromStartupInfo()
+        .incoming
+        .connectToService<ThoughtLeaker>(proxy);
 
     final response = await _attemptReadMind(proxy);
     proxy.ctrl.close();