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/server/sidebar-data.ts

@@ -9,6 +9,10 @@ import {
   type SidebarDatasetListQueryResult,
 } from "@/lib/sidebar-data";
 import type { WorkspaceSummary } from "@/lib/workspaces";
+import {
+  fetchSidebarDatasetFromMnoteWeb,
+  getMnoteWebBaseUrl,
+} from "@/lib/server/mnote-web";
 
 type LoadSidebarDataFromConvexInput = {
   client: ConvexHttpClient;
@@ -57,9 +61,15 @@ export async function loadSidebarDataFromConvex(
     };
   }
 
-  const sidebarDataset = (await input.client.query(sidebarDatasetListQuery, {
-    workspaceId: targetWorkspaceId,
-  })) as SidebarDatasetListQueryResult;
+  const sidebarDataset = getMnoteWebBaseUrl()
+    ? (
+        await fetchSidebarDatasetFromMnoteWeb({
+          workspaceId: targetWorkspaceId,
+        })
+      ).dataset
+    : ((await input.client.query(sidebarDatasetListQuery, {
+        workspaceId: targetWorkspaceId,
+      })) as SidebarDatasetListQueryResult);
   const normalizedDocuments = (sidebarDataset.documents ?? []) as DocumentRecord[];
 
   return {