Add MCP tab to Agentic UI settings with copyable server config

[bcotrim]

Related issues

• Related to STU-1882

How AI was used in this PR

Implemented with Claude Code (part of the STU-1882 settings series), guided by the exploration in #3979. Code, styles, and tests were reviewed before pushing;

Proposed Changes

• Adds an MCP tab to the Agentic UI settings so users can connect external AI assistants to Studio without hunting through docs: a short explanation of what MCP is for, a "Learn more" link to the Studio MCP docs, and the ready-to-paste wordpress-studio server configuration JSON with a one-click copy button.
• The copy button now only shows "Copied" after the text has actually landed on the clipboard, and announces it to screen readers. If copying fails, the button no longer claims success — this also fixes the same silent-failure behavior for copying chat messages and markdown code blocks, which shared the button.

Testing Instructions

1. Launch Studio with the Agentic UI enabled and open Settings.
2. Switch to the new MCP tab: verify the intro text, the "Learn more" link (opens the MCP docs in your browser), and the config JSON code block.
3. Click the copy icon over the code block: a "Copied" check state should appear for ~2s, and pasting should produce the JSON.
4. Check the tab in both light and dark mode.
5. Copying a chat message or a markdown code block in a session should still work as before.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing 6037788 vs trunk

app-size

Metric	trunk	6037788	Diff	Change
App Size (Mac)	1355.67 MB	1355.67 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	6037788	Diff	Change
load	1037 ms	1094 ms	+57 ms	🔴 5.5%

site-startup

Metric	trunk	6037788	Diff	Change
siteCreation	7020 ms	7023 ms	+3 ms	⚪ 0.0%
siteStartup	2352 ms	2846 ms	+494 ms	🔴 21.0%

---

Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)

[sejas]

Looks good! thanks for adding the MCP information to the Agentic UI.

Light	Dark	Dark RTL