feat: add BASE_PATH env var for serving UI from a subpath

When BASE_PATH is set (e.g., /server/), the entrypoint script injects
a <base> tag and rewrites asset paths in index.html. React Router reads
the basename from the <base> tag. Vite builds with relative paths.
Default / for standalone mode (no changes).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

ui/vite.config.ts

@@ -27,6 +27,7 @@ export default defineConfig({
   optimizeDeps: {
     include: ['swagger-ui-dist/swagger-ui-bundle'],
   },
+  base: './',
   build: {
     outDir: 'dist',
   },