docs: Fix *Join Zulip Chat button* doc.

With tweaks from tabbott to clean it up and better explain it.

templates/zerver/help/chat-with-zulip-button.md

@@ -1,11 +1,19 @@
-# **Chat button for zulip**
-* This button redirects user to zulip chat [Zulip Chat Portal for Developers](https://chat.zulip.org).
-* This is displayed in Zulip's [GitHub](https://github.com/zulip/zulip) README.md page.
-* To embed this badge, simply copy and paste the following markdown:
+# Join Zulip chat badge
 
-~~~
-[![Zulip chat](https://img.shields.io/badge/zulip-join_chat-brightgreen.svg)](https://chat.zulip.org)
-~~~
+If you'd like to link to your Zulip organization in your project's
+documentation or GitHub homepage, you can do that with our
+[shields.io](https://shields.io) badge:
+[![](https://img.shields.io/badge/zulip-join_chat-brightgreen.svg)](https://chat.zulip.org)
 
-* This badge is dynamically generated, visit shields.io for detail information about customizing it.
-* A static version is available in `/static/images/help/chat_on_zulip.[png|svg]`.
+To embed this badge in a Markdown document, simply copy and paste the
+following Markdown, replacing `https://chat.zulip.org` with the URL of
+your Zulip server:
+
+```
+[![](https://img.shields.io/badge/zulip-join_chat-brightgreen.svg)](https://chat.zulip.org)
+```
+
+!!! tip ""
+    This badge is dynamically generated; visit
+    [shields.io](https://shields.io) for detailed information about
+    customizing it.

templates/zerver/help/index.md

@@ -151,8 +151,5 @@ as an **organization**.
 * [Add someone to a stream](/help/add-or-invite-someone-to-a-stream)
 * [Remove someone from a stream](/help/remove-someone-from-a-stream)
 
----
-
-# Include Zulip
-
-* [Chat with zulip button](/help/chat-with-zulip-button)
+## Linking to a Zulip server
+* [Join Zulip chat badge](/help/chat-with-zulip-button)