feat: Add Project Management Node sample

node/project-management-app/.gcloudignore

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+# This file specifies files that are *not* uploaded to Google Cloud
+# using gcloud. It follows the same syntax as .gitignore, with the addition of
+# "#!include" directives (which insert the entries of the given .gitignore-style
+# file at that point).
+#
+# For more information, run:
+#   $ gcloud topic gcloudignore
+#
+.gcloudignore
+# If you would like to upload your .git directory, .gitignore file or files
+# from your .gitignore file, remove the corresponding line
+# below:
+.git
+.gitignore
+
+node_modules

node/project-management-app/README.md

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+# Google Chat Project Management app
+
+This code sample shows how to make a Google Chat app that a team can use to
+manage projects in real time.
+
+The Chat app is implemented as a Google Cloud Function using a Node.js runtime,
+which responds to
+[interaction events](https://developers.google.com/chat/api/guides/message-formats/events)
+from Google Chat.
+
+It uses [Vertex AI](https://cloud.google.com/vertex-ai) to help teams write user
+stories (which represent features of a software system from the point of view of
+a user for the team to develop) and persists the stories in a
+[Firestore](https://firebase.google.com/docs/firestore) database.
+
+## Tutorial
+
+For detailed instructions to deploy and run this sample, follow the tutorial
+[Manage projects with Google Chat, Vertex AI, and Cloud Firestore](https://developers.google.com/chat/tutorial-project-management)
+in the Google Chat developer documentation.