docs(shell-docs): add CopilotKit Skills section to build-with-agents page (CopilotKit#5039)

## Summary

Adds the Skills installation section to the shell-docs
`/build-with-agents` page

## Changes


**`showcase/shell-docs/src/content/snippets/shared/guides/build-with-agents.mdx`**
(new)
- Single source of truth for the page content
- Intro paragraph, `## CopilotKit Skills` section (Callout + Steps:
install + starter prompt), `<MCPSetup />` as second section

**`showcase/shell-docs/src/content/docs/build-with-agents.mdx`**
- Replaced inline content with `<BuildWithAgents />` — delegates to the
shared snippet
- Icon updated to `BrainCircuit`, description updated to keyword-rich
copy, `hideTOC: true` removed


**`showcase/shell-docs/src/content/docs/integrations/built-in-agent/build-with-agents.mdx`**
- Replaced `<SharedContent />` with `<BuildWithAgents />` so the skills
section appears here too (built-in-agent uses `docs_mode: authored` and
never falls through to the root page)


**`showcase/shell-docs/src/content/snippets/shared/guides/mcp-server-setup.mdx`**
- `## Overview` → `## MCP Docs Server`

**`showcase/shell-docs/src/lib/docs-render.tsx`** +
**`mdx-registry.tsx`**
- Register `BuildWithAgents` in `SNIPPET_MAP` and component registry

## Acceptance criteria status

- [x] `/coding-agents` redirects to `/build-with-agents` (PR CopilotKit#5023)
- [x] React Native moved to Platforms section (PR CopilotKit#4927 / CopilotKit#5023)
- [x] `npx skills add` flow documented with skills link and starter
prompt
- [x] MCP server install instructions present (existing content, now
labeled correctly)
- [x] Page structure follows Mastra "Build with AI" reference

Author: onsclom

showcase/shell-docs/src/content/docs/build-with-agents.mdx

@@ -1,7 +1,6 @@
 ---
 title: "Build with agents"
-icon: "lucide/Code"
-description: "Use our MCP server to connect your AI agents and backends to CopilotKit."
-hideTOC: true
+icon: "lucide/BrainCircuit"
+description: "Give your AI coding agent up-to-date knowledge of CopilotKit's APIs, patterns, and best practices."
 ---
-<MCPSetup />
+<BuildWithAgents />

showcase/shell-docs/src/content/docs/integrations/built-in-agent/build-with-agents.mdx

@@ -1,8 +1,6 @@
 ---
 title: "Build with agents"
-icon: "lucide/Code"
-description: "Use our MCP server to connect your Built-in Agent to CopilotKit."
+icon: "lucide/BrainCircuit"
+description: "Give your AI coding agent up-to-date knowledge of CopilotKit's APIs, patterns, and best practices."
 ---
-import SharedContent from "@/snippets/shared/coding-agents.mdx";
-
-<SharedContent components={props.components} />
+<BuildWithAgents />

showcase/shell-docs/src/content/snippets/shared/guides/build-with-agents.mdx

@@ -0,0 +1,39 @@
+AI coding agents may not have up-to-date knowledge of CopilotKit's APIs, patterns, and best practices. The resources on this page give them accurate, current knowledge directly in their context.
+
+## CopilotKit Skills
+
+Skills are folders of instructions, references, and scripts that coding agents can discover and use to work with CopilotKit accurately. Installing them gives your agent authoritative guidance on setup, development, debugging, integration, and upgrades — without relying on potentially outdated training data.
+
+<Callout type="info">
+  Skills are the recommended way to give your agent CopilotKit knowledge. They work natively in Claude Code, Cursor, Codex, Gemini CLI, and any tool supporting the [agentskills.io](https://agentskills.io) standard.
+</Callout>
+
+<Steps>
+  <Step>
+    ### Install the skills
+
+    Run the following command to install CopilotKit skills into your agent environment:
+
+    ```bash
+    npx skills add CopilotKit/CopilotKit
+    ```
+
+    This pulls the latest skills directly from the CopilotKit repository and installs them into your tool's skills directory (e.g. `~/.claude/skills/` for Claude Code). The CopilotKit MCP server is also auto-wired so your agent has live documentation access.
+
+    Skills cover project setup, building AI features, connecting agent frameworks, debugging, and version upgrades. The full list is in the [CopilotKit skills directory](https://github.com/CopilotKit/CopilotKit/tree/main/skills).
+
+  </Step>
+  <Step>
+    ### Start building
+
+    Open a new agent session and use a starter prompt to put the skills to work:
+
+    ```
+    Help me build a CopilotKit app. Use the copilotkit-setup skill to get started.
+    ```
+
+    Your agent will discover the installed skills and use the right one for each task — setup, development, debugging, or integration.
+  </Step>
+</Steps>
+
+<MCPSetup />

showcase/shell-docs/src/content/snippets/shared/guides/mcp-server-setup.mdx

@@ -1,4 +1,4 @@
-## Overview
+## MCP Docs Server
 
 The CopilotKit MCP server equips AI coding agents with deep knowledge about CopilotKit's APIs, patterns, and best practices. When connected to your
 development environment, it enables AI assistants to:

showcase/shell-docs/src/lib/docs-render.tsx

@@ -769,6 +769,7 @@ export const SNIPPET_MAP: Record<string, string> = {
   A2UI: "shared/generative-ui/a2ui.mdx",
   AgUI: "shared/backend/ag-ui.mdx",
   AGUI: "shared/backend/ag-ui.mdx", // alias of AgUI
+  BuildWithAgents: "shared/guides/build-with-agents.mdx",
   CodingAgents: "shared/coding-agents.mdx",
   CommonIssues: "shared/troubleshooting/common-issues.mdx",
   CopilotRuntime: "copilot-runtime.mdx",

showcase/shell-docs/src/lib/mdx-registry.tsx

@@ -541,6 +541,7 @@ export const docsComponents = {
     />
   ),
   InstallSDKSnippet: stubWithPartial("InstallSDKSnippet"),
+  BuildWithAgents: stubWithPartial("BuildWithAgents"),
   MCPApps: stubWithPartial("MCPApps"),
   MCPSetup: stubWithPartial("MCPSetup"),
   Overview: stubWithPartial("Overview"),