fix BASE_PATH routing: nginx template + runtime HTML injection

- nginx.conf → nginx.conf.template with ${BASE_PATH} in all locations
- NGINX_ENVSUBST_FILTER=BASE_PATH so nginx vars ($host, $uri) are preserved
- Entrypoint injects BASE_PATH into frontend HTML/JS (%%BASE_PATH%% → actual)
- Fixes: /test routes falling through to static SPA, %%BASE_PATH%% visible in URL

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

docker-entrypoint.sh

@@ -9,6 +9,17 @@
 
 set -e
 
+# Inject BASE_PATH into frontend HTML/JS at runtime
+if [ -n "${BASE_PATH}" ]; then
+    echo "🔧 Injecting BASE_PATH=${BASE_PATH} into frontend assets..."
+    find /usr/share/nginx/html -type f \( -name '*.html' -o -name '*.js' \) \
+        -exec sed -i "s|%%BASE_PATH%%|${BASE_PATH}|g" {} +
+else
+    # No prefix — strip the placeholder entirely
+    find /usr/share/nginx/html -type f \( -name '*.html' -o -name '*.js' \) \
+        -exec sed -i "s|%%BASE_PATH%%||g" {} +
+fi
+
 echo "🔀 Starting Switchboard Core backend..."
 
 # Launch Go backend in background (from /app so migrations are found)