fix(ai): JSONL fallback also detects duplicate ids inside the payload

Prior precheck only compared the JSONL payload's ids against the live
doc — it didn't detect duplicates within the payload itself. A model
emitting the same id twice (two roots sharing an id, a nested child
reusing a root id, etc) would still slip past: addNode appends both
copies, getNodeById returns the first match for both verifies, and a
later rollback removeNode would delete only one of the two duplicates,
leaving an orphan with the same id in the doc.

Detect internal duplicates during the same id-collection pass:
collectIds tracks `treeIds` as a Set and pushes any id seen twice into
`internalDuplicates`. If non-empty, return `failed` immediately with
the duplicate list — same shape as the existing live-doc collision
branch, no doc mutation, no side effects, retry path takes over.

apps/web/src/services/ai/element-tools-dispatcher.ts

@@ -499,14 +499,38 @@ function applyBatchDesignAsJsonl(jsonl: string, ctx: DispatchContext): DispatchR
   // later rollback `removeNode(id)` would delete the pre-existing node
   // instead of the freshly-added duplicate. Detect collisions before
   // mutating the doc so we can fail cleanly without side effects.
+  //
+  // Two collision sources to guard:
+  //   1. Internal: the JSONL payload itself contains the same id twice
+  //      (two roots with the same id, a nested child reusing a root id,
+  //      etc) — addNode would append both copies and confuse the verify
+  //      / rollback path the same way as a live-doc collision.
+  //   2. External: an id in the payload already exists in the live doc.
   const treeIds = new Set<string>();
+  const internalDuplicates: string[] = [];
   const collectIds = (n: PenNode) => {
-    treeIds.add(n.id);
+    if (treeIds.has(n.id)) {
+      internalDuplicates.push(n.id);
+    } else {
+      treeIds.add(n.id);
+    }
     if ('children' in n && Array.isArray((n as PenNode & { children?: PenNode[] }).children)) {
       for (const child of (n as PenNode & { children: PenNode[] }).children) collectIds(child);
     }
   };
   for (const root of tree) collectIds(root);
+  if (internalDuplicates.length > 0) {
+    const list = `${internalDuplicates.slice(0, 4).join(', ')}${internalDuplicates.length > 4 ? '…' : ''}`;
+    return {
+      status: 'failed',
+      route: 'batch-design-dsl',
+      toolName: 'batch_design',
+      message:
+        `batch_design.operations JSONL has ${internalDuplicates.length} duplicate id(s) within ` +
+        `the payload itself: ${list}. Refusing to insert — doc state preserved.`,
+      insertedNodes: [],
+    };
+  }
   const collisions: string[] = [];
   for (const id of treeIds) {
     if (store.getNodeById(id)) collisions.push(id);