docs: edit build with AI page to reflect changes in MCP

[patrikbraborec]

The Apify MCP Server will not require auth for documentation tools (apify/apify-mcp-server#341). This PR makes changes regarding to it - mainly improvements to the Build with AI page.

I also checked the Apify MCP Server documentation page, but I do not see a good place, where we should mention that documentation tools do not need auth (it would probably add confusion).

I plan to update mcp.apify.com page, and also will discuss whatever we will add the following option to AI Dropdown: #2079.

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Note

Updates the Build with AI guide with MCP server setup for Claude, Cursor, and VS Code, and removes the unused InstallMCPButton component and styles.

• Docs (build-with-ai):
  • Add setup instructions for Apify MCP Server in Claude, Cursor (with mcp.json snippet), and VS Code using https://mcp.apify.com/?tools=docs.
  • Streamline MCP configuration note and improve guidance for providing context via Copy for LLM and /llms.txt.
  • Remove unused InstallMCPButton import.
• Cleanup:
  • Delete src/components/InstallMCPButton.jsx and src/components/InstallMCPButton.module.css.

^{Written by Cursor Bugbot for commit 5e93989. Configure here.}

[apify-service-account]

Preview for this PR was built for commit 5e93989 and is ready at https://pr-2119.preview.docs.apify.com!

[apify-service-account]

Preview for this PR was built for commit 5867d5f and is ready at https://pr-2119.preview.docs.apify.com!