Broken UI when using custom path in 2.50.0

[lukeraus]

Describe the bug
This bug is still present
originally in: #3183
Reported again here: #3325

The UI breaks when using a custom publicPath when using 2.48.1 and up.
Was fixed in 2.47.3
And still present in 2.50.0

To Reproduce
Steps to reproduce the behavior:

1. Update config and set publicPath (env TEMPORAL_UI_PUBLIC_PATH) to /custom
2. Deploy temporal/ui 2.50.0
3. Navigate to the UI and click around.
4. The URL includes path twice. e.g., http://my-temporal-ui/custom/custom

Expected behavior
The URL should only contains publicPath once.

Screenshots

Desktop (please complete the following information):
OS: MacOS 26.5
Browser: Chrome 148.0.7778.168

Additional context
Add any other context about the problem here.