feat(tree): server-authoritative realtime tree updates

The sidebar page tree only updated on other clients when a change was made
via the UI tree, in an open tab, within a ~50ms client relay window — API/MCP/
AI/import changes never propagated. Move the source of truth to the server.

Server:
- Enrich PageEvent with thin TreeNodeSnapshot(s) so the WS listener never reads
  the DB (avoids the in-transaction visibility race). insertPage fills the
  create snapshot from its returning() row; removePage ships only the deleted
  subtree ROOT (client treeModel.remove drops descendants); restorePage carries
  spaceId.
- New PAGE_MOVED event from movePage with old/new parent + position + snapshot
  (generic PAGE_UPDATED stays for content/rename).
- WsService.emitTreeEvent mirrors emitCommentEvent (per-space restriction gate:
  spaceHasRestrictions -> hasRestrictedAncestor -> broadcastToAuthorizedUsers);
  author NOT excluded so non-UI creators see their own page (receiver is
  idempotent).
- WsTreeService.broadcastPageCreated/Deleted/Moved + broadcastRefetchRoot;
  new PageWsListener (create/delete/move/restore) registered in WsModule.

Client:
- Remove the client relay (emit + setTimeout(50)) from create/move/delete;
  keep optimistic local updates. Make the optimistic create insert id-idempotent
  (find-then-skip) so the now-fast server addTreeNode broadcast can't race it
  into a duplicate row. addTreeNode inserts by fractional position among loaded
  siblings (consistent order across clients).

Restore uses refetchRootTreeNodeEvent (robust for subtree re-attach). Rename/icon
updateOne and cross-space move realtime are deferred (commented as follow-ups).

Implements docs/backlog/realtime-tree-server-authoritative.md.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

apps/client/src/features/websocket/use-tree-socket.ts

@@ -54,13 +54,17 @@ export const useTreeSocket = () => {
           break;
         case "addTreeNode":
           setTreeData((prev) => {
+            // Idempotent: the author already inserted the node optimistically,
+            // and a node may be re-delivered — never insert a duplicate id.
             if (treeModel.find(prev, event.payload.data.id)) return prev;
             const newParentId = event.payload.parentId as string | null;
-            let next = treeModel.insert(
+            // Insert by `position` among already-loaded siblings (not the
+            // sender's absolute index) so order is consistent across clients
+            // with different loaded sets.
+            let next = treeModel.insertByPosition(
               prev,
               newParentId,
               event.payload.data,
-              event.payload.index,
             );
             // Mirror the emitter: flip new parent's hasChildren to true so
             // the chevron renders on the receiver.