[BUG] Browser pane: local HTML files lose JavaScript (outside project) or the Clipboard API (inside project), with no indication to the user

Environment
Claude desktop 2.31226.0 (Code tab), Claude Code 2.1.289, macOS 27.0.1, Apple Silicon.

What happens
Claude often delivers work as a self-contained interactive HTML file (copy buttons, checkboxes). Opened in the built-in Browser pane, those controls silently do nothing.

1. File outside the session's project folder (e.g. ~/Downloads): the pane renders it as a static snapshot. No scripts run. The tool result says "files outside the project folder render as static snapshots", but nothing in the pane tells the user.
2. File inside the project folder: scripts run and click handlers fire, but the document is loaded as a data: URL (location.protocol === "data:", origin === "null", isSecureContext === false), so navigator.clipboard is undefined and "Copy" buttons fail.

Repro
Save this as test.html, open it in the Browser pane from inside and from outside the project folder:

<p id="inline">INLINE SCRIPT: did not run</p>
<button onclick="navigator.clipboard.writeText('x').then(()=>this.textContent='copied')">Copy</button>
<script>document.getElementById('inline').textContent='INLINE SCRIPT: ran'</script>

• Outside the project: the text stays "did not run".
• Inside the project: the text says "ran"; clicking Copy throws "Cannot read properties of undefined (reading 'writeText')".
• In Chrome via file://: both work.

Expected
Either local files get a context where the Clipboard API works, or the pane shows a visible notice ("scripts are disabled for this file — open in your browser") so the page doesn't look broken.