Keep broker path in API CI public URL

.github/workflows/tests.yml

@@ -228,7 +228,7 @@ jobs:
           set -euo pipefail
           cp .github/ci.env .env
           cp .github/ci.env.staging .env.staging
-          printf '\nEDGE_PUBLIC_BROKER_URL=http://localhost:%s\n' "$EDGE_BROKER_CI_PORT" >> .env
+          printf '\nEDGE_PUBLIC_BROKER_URL=http://localhost:%s/edge-broker\n' "$EDGE_BROKER_CI_PORT" >> .env
 
       - name: Setup Node.js
         uses: actions/setup-node@v4

scripts/edge-gateway-e2e.mjs

@@ -117,6 +117,10 @@ function resolveBrokerWebSocketUrl(rawUrl, apiBaseUrl) {
     websocketUrl.pathname = `/api/edge-broker${brokerPath}`;
   }
 
+  if (isLocalHost(websocketUrl.hostname)) {
+    websocketUrl.pathname = websocketUrl.pathname.replace(/^\/edge-broker(?=\/|$)/, "") || "/";
+  }
+
   return websocketUrl.toString();
 }