Add iframe auto-resize via postMessage

Embeds now report content height to the parent frame using a
ResizeObserver on document.body. The EmbedDialog snippet includes
a listener script that adjusts the iframe height on each resize
event. Documented the spicebook-resize protocol in llms.txt.

frontend/public/llms.txt

@@ -598,6 +598,26 @@ iframe.contentWindow.postMessage(
 
 Accepted values for `theme`: `"dark"`, `"light"`. Other messages are ignored.
 
+### Auto-resize via postMessage
+
+The embed reports its content height to the parent page whenever the layout changes (initial render, simulation results, expanded cells). The parent listens for `spicebook-resize` messages and updates the iframe height:
+
+```javascript
+window.addEventListener('message', function(e) {
+  if (e.data && e.data.type === 'spicebook-resize') {
+    document.getElementById('spicebook-{notebook_id}').style.height = e.data.height + 'px';
+  }
+});
+```
+
+The message payload:
+
+```json
+{ "type": "spicebook-resize", "height": 1842 }
+```
+
+`height` is `document.documentElement.scrollHeight` in pixels. The embed sends this message on every `ResizeObserver` callback, deduplicated to only fire when height actually changes. The **Embed** button's generated snippet includes this listener automatically.
+
 ### Discovering the embed snippet
 
-In the notebook editor UI, the **Embed** button in the toolbar opens a popover with a ready-to-copy iframe snippet and a theme toggle.
+In the notebook editor UI, the **Embed** button in the toolbar opens a popover with a ready-to-copy iframe snippet (including auto-resize listener) and a theme toggle.

frontend/src/components/embed/EmbedViewer.tsx

@@ -38,6 +38,26 @@ export default function EmbedViewer({ notebookId, initialTheme }: EmbedViewerPro
     return () => window.removeEventListener('message', handleMessage);
   }, []);
 
+  // Report content height to parent frame for auto-resize
+  useEffect(() => {
+    if (typeof window === 'undefined' || window.parent === window) return;
+
+    let lastHeight = 0;
+    function reportHeight() {
+      const height = document.documentElement.scrollHeight;
+      if (height !== lastHeight) {
+        lastHeight = height;
+        window.parent.postMessage({ type: 'spicebook-resize', height }, '*');
+      }
+    }
+
+    const observer = new ResizeObserver(reportHeight);
+    observer.observe(document.body);
+    reportHeight();
+
+    return () => observer.disconnect();
+  }, []);
+
   // Keep a ref to notebook for use inside handleRun to avoid stale closures
   const notebookRef = useRef(notebook);
   notebookRef.current = notebook;

frontend/src/components/notebook/toolbar/EmbedDialog.tsx

@@ -14,12 +14,23 @@ export function EmbedDialog() {
 
   const origin = typeof window !== 'undefined' ? window.location.origin : '';
 
+  const iframeId = `spicebook-${notebookId}`;
+
   const snippet = `<iframe
+  id="${iframeId}"
   src="${origin}/embed/${notebookId}?theme=${theme}"
   width="100%" height="600"
   style="border: 1px solid #334155; border-radius: 8px;"
   allow="clipboard-write"
-></iframe>`;
+></iframe>
+<script>
+window.addEventListener('message', function(e) {
+  if (e.data && e.data.type === 'spicebook-resize') {
+    var f = document.getElementById('${iframeId}');
+    if (f) f.style.height = e.data.height + 'px';
+  }
+});
+</script>`;
 
   function handleCopy() {
     navigator.clipboard.writeText(snippet).then(() => {
@@ -72,7 +83,7 @@ export function EmbedDialog() {
           <textarea
             readOnly
             value={snippet}
-            rows={5}
+            rows={12}
             className="w-full resize-none rounded-md border border-slate-600 bg-slate-800 p-2 font-mono text-[11px] text-slate-300 focus:outline-none focus:border-blue-500"
           />