[router]: Add Embedding routing logic (#10129)

Signed-off-by: Jintao Zhang <zhangjintao9020@gmail.com>
Co-authored-by: Waël Boukhobza <wawa_wael@live.fr>

sgl-router/py_test/e2e/test_e2e_embeddings.py

@@ -0,0 +1,38 @@
+from types import SimpleNamespace
+
+import pytest
+import requests
+
+
+@pytest.mark.e2e
+def test_embeddings_basic(
+    e2e_router_only_rr, e2e_primary_embedding_worker, e2e_embedding_model
+):
+    base = e2e_router_only_rr.url
+    worker_url = e2e_primary_embedding_worker.url
+
+    # Attach embedding worker to router-only instance
+    r = requests.post(f"{base}/add_worker", params={"url": worker_url}, timeout=180)
+    r.raise_for_status()
+
+    # Simple embedding request with two inputs
+    payload = {
+        "model": e2e_embedding_model,
+        "input": [
+            "the quick brown fox",
+            "jumps over the lazy dog",
+        ],
+    }
+    r = requests.post(f"{base}/v1/embeddings", json=payload, timeout=120)
+
+    assert r.status_code == 200, f"unexpected status: {r.status_code} {r.text}"
+
+    data = r.json()
+    assert "data" in data and isinstance(data["data"], list)
+    assert len(data["data"]) == 2
+
+    # Validate shape of embedding objects
+    for item in data["data"]:
+        assert "embedding" in item and isinstance(item["embedding"], list)
+        # Ensure non-empty vectors
+        assert len(item["embedding"]) > 0