#34916 Inconsistency in custom favicon: favicon set via UI Theme Customization is not applied to the browser tab
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate.
### What happened?
On the UI Theme Customization page, LiteLLM lets a user set a Custom Favicon URL to override the default favicon. However, after setting a valid Custom Favicon URL and saving the changes, the browser tab continues to display the default LiteLLM favicon instead of the custom one that was configured.
The Custom Logo appears to apply correctly, but the Custom Favicon does not — so there is an inconsistency between the saved favicon setting and what is actually rendered in the browser tab.
Expected: The browser tab favicon should update to reflect the configured Custom Favicon URL.
Actual: The browser tab favicon still shows the default LiteLLM icon, ignoring the saved custom favicon setting.
Note: A hard refresh / cache clear did not resolve it, which suggests the custom favicon is not being injected into the page's <head>.
### Steps to Reproduce
1. Go to the admin dashboard → UI Theme Customization. 2. Enter a valid image URL (.png) in the "Custom Favicon URL" field. 3. Click "Save Changes". 4. Reload / open the dashboard and observe the br…