Add required test suite and websocket fixes

tests/test_ws_admin.py

@@ -1,2 +1,38 @@
-def test_placeholder_ws_admin():
-    assert True
+import pytest
+from starlette.websockets import WebSocketDisconnect
+
+from conftest import admin_login, create_session, join_student
+
+
+def test_instructor_ws_requires_admin_cookie(client, sample_pool):
+    sid = create_session(client, sample_pool)
+    client.cookies.clear()
+    with pytest.raises(WebSocketDisconnect) as exc:
+        with client.websocket_connect(f"/ws/instructor/{sid}"):
+            pass
+    assert exc.value.code == 4001
+
+
+def test_instructor_controls_transition_and_broadcast(client, sample_pool):
+    sid = create_session(client, sample_pool)
+    join_student(client, sid, "s1", "Student One")
+    admin_login(client)
+    with client.websocket_connect(f"/ws/student/{sid}") as student_ws:
+        assert student_ws.receive_json()["type"] == "state"
+        with client.websocket_connect(f"/ws/instructor/{sid}") as admin_ws:
+            assert admin_ws.receive_json()["type"] == "state"
+            assert admin_ws.receive_json()["type"] == "lobby_update"
+            admin_ws.send_json({"type": "open_question", "question_idx": 0, "time_limit": 2})
+            student_open = student_ws.receive_json()
+            assert student_open["type"] == "question_open"
+            admin_open = admin_ws.receive_json()
+            assert admin_open["type"] == "question_open"
+            assert admin_ws.receive_json()["type"] == "live_histogram"
+
+            admin_ws.send_json({"type": "close_question"})
+            assert student_ws.receive_json()["type"] == "question_closed"
+            messages = [admin_ws.receive_json(), admin_ws.receive_json()]
+            assert {msg["type"] for msg in messages} == {"question_closed", "full_leaderboard"}
+
+            admin_ws.send_json({"type": "next"})
+            assert student_ws.receive_json()["type"] == "between_questions"