feat(ui): support custom basePath

[penge]

Support custom basePath.

Ensure the correct API URL is constructed when called from either the server or the client.

How to test (development)

1. Set:

NEXT_PUBLIC_BASE_PATH='/granite/playground'

2. Run:

$ mise beeai-ui:run:dev

3. Open: http://localhost:3000/granite/playground

---

How to test (build)

1. Set:

NEXT_PUBLIC_BASE_PATH='/granite/playground'

2. Run:

$ mise beeai-ui:build:nextjs
$ mise beeai-ui:run

3. Open: http://localhost:3000/granite/playground

Expectations

• API calls use the correct base path and work (both "ACP" and "API").
• Favicon correctly set.