Vibe Start

You are adding the Clad Support Chat widget to this web application.
 
First, read the official documentation (fetch these URLs before writing code):
- Docs index:  https://docs.useclad.ai/llms.txt
- Full docs:   https://docs.useclad.ai/llms-full.txt
- Quickstart:  https://docs.useclad.ai/quickstart.md
Every page is available as Markdown by appending .md to its URL
(for example https://docs.useclad.ai/installation.md).
 
My credentials:
- Workspace ID: {YOUR_WORKSPACE_ID}
- Widget ID:    {YOUR_WIDGET_ID}
 
Then implement the integration:
1. Detect this project's framework (plain HTML, React, Next.js, Vue, etc.).
2. Install the widget using the single <script> snippet from the Quickstart.
   Do NOT use npm or any package manager — there is no package. The script
   loads from https://clad-server-staging.up.railway.app/widget/v1/widget.js.
   Add it once in the app shell so it runs
   on every page (e.g. index.html just before </body>, the Next.js root layout
   via next/script, or your framework's equivalent).
3. Set window.SupportChatSettings with my Workspace ID and Widget ID.
4. If this app has logged-in users, also set up identity verification:
   - Add a backend endpoint that returns a short-lived (<= 15 min) HS256 JWT,
     signed with a SUPPORT_CHAT_WIDGET_SECRET environment variable, including
     the claims described on the Identity verification page (sub, email, name,
     workspace_id, widget_id, exp).
   - Wire the SDK's tokenProvider to that endpoint, call identify() on login,
     and shutdown({ clearStorage: true }) on logout. Use the framework recipe
     that matches this codebase.
5. Follow the Security best practices page: never expose the widget secret in
   frontend code, keep tokens short-lived, and remind me to add my site's
   origin to the widget's allowed origins.
6. Do not hardcode secrets; read them from environment variables.
7. When done, summarize the files you changed and tell me exactly how to test
   that the launcher appears and that a test message reaches the support inbox.
 
Keep the integration minimal and idiomatic for this codebase.