feat(kernel): finish phase3 bridge cutover and phase4 tree projection

- add generic mnote-web query transport and bridge routes for workspace/request/trace

- route sidebar compat traffic through mnote-web and tighten fixture fallback to dev/test

- unify sidebar/page tree/file tree/picker consumers on page_tree projection

- sync phase3/phase4 checklist, breakdown docs, and harness progress state

wolai-frontend/src/lib/sidebar-data.ts

@@ -51,7 +51,7 @@ export type SidebarDatasetListQueryResult = {
   active_workspace_id: string;
   workspaces: WorkspaceSummary[];
   documents: DocumentRecord[];
-  kernel_sidebar_projection?: KernelSidebarProjection | null;
+  kernel_sidebar_projection: KernelSidebarProjection;
   trashed_documents: SidebarInitialData["trashedDocuments"];
   media_assets: MediaAsset[];
   trashed_media_assets: MediaAsset[];
@@ -241,16 +241,14 @@ export function buildSidebarDatasetListQueryResult(
 export function mapSidebarDatasetListQueryResultToInitialData(
   result: SidebarDatasetListQueryResult,
 ): SidebarInitialData {
-  const kernelSidebarProjection =
-    result.kernel_sidebar_projection ?? buildKernelSidebarProjection(result.documents);
   return {
     activeWorkspaceId: result.active_workspace_id,
     workspaces: [...result.workspaces],
     documents: [...result.documents],
-    kernelSidebarProjection,
+    kernelSidebarProjection: result.kernel_sidebar_projection,
     kernelSidebarTree: buildSidebarTreeFromKernelProjection({
       records: result.documents,
-      projection: kernelSidebarProjection,
+      projection: result.kernel_sidebar_projection,
     }),
     trashedDocuments: [...result.trashed_documents],
     trashedMediaAssets: [...result.trashed_media_assets],