feat: sync Pluto-side code edits into VSCode cell text

cell_inputs.<id>.code replace patches (browser UI edits, MCP
update_cell) were logged UNHANDLED — the switch case listened for
'cell_input' (singular) which never matches. The patch now rewrites the
matching cell's text, unwrapping md""" wrappers for markup cells.
Echoes of our own executeCell push are dropped by text equality, and
the remote-edit suppression (now shared via beginRemoteEdit/
endRemoteEditSoon) guards the applyEdit.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Author: pankgeorg

src/controller.ts

@@ -654,10 +654,7 @@ export class PlutoNotebookController {
       `[CellOrderSync] Applying remote structure: ${currentOrder.length} -> ${plutoOrder.length} cells`
     );
 
-    this.remoteEditDepth.set(
-      notebookPath,
-      (this.remoteEditDepth.get(notebookPath) ?? 0) + 1
-    );
+    this.beginRemoteEdit(notebookPath);
     try {
       const edit = new vscode.WorkspaceEdit();
       edit.set(notebook.uri, [
@@ -668,16 +665,71 @@ export class PlutoNotebookController {
       ]);
       await vscode.workspace.applyEdit(edit);
     } finally {
-      // Change events may be delivered after applyEdit resolves — release
-      // the suppression on the next tick
-      setTimeout(() => {
-        const depth = this.remoteEditDepth.get(notebookPath) ?? 1;
-        if (depth <= 1) {
-          this.remoteEditDepth.delete(notebookPath);
-        } else {
-          this.remoteEditDepth.set(notebookPath, depth - 1);
-        }
-      }, 0);
+      this.endRemoteEditSoon(notebookPath);
+    }
+  }
+
+  private beginRemoteEdit(notebookPath: string): void {
+    this.remoteEditDepth.set(
+      notebookPath,
+      (this.remoteEditDepth.get(notebookPath) ?? 0) + 1
+    );
+  }
+
+  /**
+   * Releases remote-edit suppression on the next tick — change events may
+   * be delivered after applyEdit resolves.
+   */
+  private endRemoteEditSoon(notebookPath: string): void {
+    setTimeout(() => {
+      const depth = this.remoteEditDepth.get(notebookPath) ?? 1;
+      if (depth <= 1) {
+        this.remoteEditDepth.delete(notebookPath);
+      } else {
+        this.remoteEditDepth.set(notebookPath, depth - 1);
+      }
+    }, 0);
+  }
+
+  /**
+   * Applies a Pluto-side code edit (browser UI, MCP update_cell) to the
+   * matching VSCode cell's text. Our own executeCell pushes echo back as
+   * the same patch — the text-equality check drops those.
+   */
+  private async _applyRemoteCodeEdit(
+    notebook: vscode.NotebookDocument,
+    cellId: CellId,
+    rawCode: string
+  ): Promise<void> {
+    const cell = this.getCellByPlutoId(notebook, cellId);
+    if (!cell) {
+      return;
+    }
+    let newText = rawCode ?? "";
+    if (cell.kind === vscode.NotebookCellKind.Markup) {
+      const markdown = extractMarkdownContent(newText);
+      if (isDefined(markdown)) {
+        newText = markdown;
+      }
+    }
+    if (cell.document.getText() === newText) {
+      return;
+    }
+    const notebookPath = notebook.uri.fsPath;
+    this.beginRemoteEdit(notebookPath);
+    try {
+      const edit = new vscode.WorkspaceEdit();
+      edit.replace(
+        cell.document.uri,
+        new vscode.Range(0, 0, cell.document.lineCount, 0),
+        newText
+      );
+      await vscode.workspace.applyEdit(edit);
+      this.outputChannel.appendLine(
+        `[CodeSync] Cell ${cellId} code updated from Pluto`
+      );
+    } finally {
+      this.endRemoteEditSoon(notebookPath);
     }
   }
 
@@ -776,16 +828,23 @@ export class PlutoNotebookController {
               );
               break;
             }
-            case "cell_input": {
+            case "cell_inputs": {
               if (rest[1] === "code" && patch.op === "replace") {
-                // TODO here we need to update the code for the cell
+                void this._applyRemoteCodeEdit(
+                  notebook,
+                  rest[0] as CellId,
+                  patch.value as string
+                ).catch((error) => {
+                  this.outputChannel.appendLine(
+                    `[CodeSync] Failed for ${rest[0]}: ${
+                      error instanceof Error ? error.message : String(error)
+                    }`
+                  );
+                });
               }
-
-              this.outputChannel.appendLine(
-                `[UNHANDLED] cell_input ${patch.path.join(".")} action ${
-                  patch.op
-                }`
-              );
+              // Other cell_inputs fields (cell_id, code_folded, metadata)
+              // have no document representation to update; structural
+              // add/remove is handled via cell_order sync
               break;
             }
             case "cell_results":