Switching Project won't update the UI setting page and require manual refresh

**Describe the bug**
Switching Project won't update the UI setting page, require manual refresh

**Authgear Version**
- Version: 2023-09-04

**To Reproduce**
Steps to reproduce the behavior:
1. Open random one project
2. Click on 'UI Settings'
3. Click on Logo and go back to home page
4. Open random another project
5. Click on 'UI Settings'

**Expected behavior**
Switching Project would update the UI setting page automatically

**Client Env (if applicable, please complete the following information):**
- Device: Macbook
- OS: macOS
- Browser chrome
- Browser Version 116.0.5845.140

Reproduce the issue through the reported UI Settings and Logo navigation steps while switching between projects. Trace the UI Settings page's project selection and refresh behavior; done means opening another project shows its current UI settings without a manual browser refresh.

Written by the indexing model from the issue text.