feat(core): cache navigation collapsed state (#13315)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **Refactor**
* Collapsible section state in navigation panels is now managed using a
unified path-based approach, enabling more consistent and centralized
control across desktop and mobile interfaces.
* The collapsed/expanded state of navigation sections and nodes is now
persistently tracked using hierarchical paths, improving reliability
across sessions and devices.
* Internal state management is streamlined, with local state replaced by
a shared service, resulting in more predictable navigation behavior.

* **Chores**
* Removed obsolete types and legacy section management logic for
improved maintainability.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

packages/frontend/core/src/components/root-app-sidebar/index.tsx

@@ -229,7 +229,7 @@ export const RootAppSidebar = memo((): ReactElement => {
         <NavigationPanelTags />
         <NavigationPanelCollections />
         <CollapsibleSection
-          name="others"
+          path={['others']}
           title={t['com.affine.rootAppSidebar.others']()}
           contentStyle={{ padding: '6px 8px 0 8px' }}
         >