fix: doc update time outdated (#7344)

Fix issue [BS-603](https://linear.app/affine-design/issue/BS-603).

- Move observe `blockUpdated` logic in `blocksuite-editor` component, so it can be excuted on both page-detail and center-peek mode.
- Remove useless `getDocUpdatedAt` service, because blocksuite can get `docMeta` directly.

https://github.com/toeverything/blocksuite/pull/7434

https://github.com/toeverything/AFFiNE/assets/12724894/e01e3f97-f1d0-4d1d-a8ed-e70e27e39bdb

packages/frontend/core/src/components/blocksuite/block-suite-editor/blocksuite-editor.tsx

@@ -88,6 +88,17 @@ const BlockSuiteEditorImpl = forwardRef<AffineEditorContainer, EditorProps>(
       [onLoadEditor, ref]
     );
 
+    useEffect(() => {
+      const disposable = page.slots.blockUpdated.once(() => {
+        page.collection.setDocMeta(page.id, {
+          updatedDate: Date.now(),
+        });
+      });
+      return () => {
+        disposable.dispose();
+      };
+    }, [page]);
+
     useEffect(() => {
       return () => {
         editorDisposeRef.current();

packages/frontend/core/src/components/page-detail-editor.tsx

@@ -75,13 +75,6 @@ const PageDetailEditorMain = memo(function PageDetailEditorMain({
       // debug current detail editor
       globalThis.currentEditor = editor;
       const disposableGroup = new DisposableGroup();
-      disposableGroup.add(
-        page.slots.blockUpdated.once(() => {
-          page.collection.setDocMeta(page.id, {
-            updatedDate: Date.now(),
-          });
-        })
-      );
       localStorage.setItem('last_page_id', page.id);
 
       if (onLoad) {