feat(web): expose health + turns_left in InteractiveSession.state()

Adds two additive keys to the state() dict: health (= game.health, 0
for non-health scenarios) and turns_left (= play_turns - len(turns)).
Covered by tests/web/test_errand_web.py (3 new tests); all 34 web
tests pass.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

proteus/game/runtime/interactive.py

@@ -72,6 +72,8 @@ class InteractiveSession:
             "phase": phase,
             "turn_idx": played,
             "play_turns": self._play_turns,
+            "health": self._game.health,
+            "turns_left": max(0, self._play_turns - len(self._turns)),
             "grid": core.grid_to_list(self._game.current_grid()),
             "legend": {str(k): v for k, v in self._scenario.legend().items()},
             "actions": list(self._scenario.action_set),

tests/web/test_errand_web.py

@@ -0,0 +1,40 @@
+"""errand_runner over the web: state exposes health/turns_left + interact action;
+the handover memory renders frames (visual-only objects)."""
+from proteus.web.local.server import handle_request
+
+
+def test_session_state_exposes_health_and_turns_left():
+    registry = {}
+    status, payload, _ = handle_request(
+        "POST", "/session",
+        {"scenario": "errand_runner", "seed": 7, "play_turns": 30}, registry,
+    )
+    assert status == 200
+    st = payload["state"]
+    assert st["health"] == 6
+    assert st["turns_left"] == 30
+    assert "interact" in st["actions"]
+
+
+def test_errand_memory_frames_present():
+    registry = {}
+    _s, payload, _c = handle_request(
+        "POST", "/session",
+        {"scenario": "errand_runner", "seed": 7, "play_turns": 30}, registry,
+    )
+    mem = payload["memory"]
+    assert mem["attached"] is True
+    assert len(mem["frames"]) >= 1          # the persona demonstration replays
+    assert mem["persona"] in {"civic", "opportunist", "warm_outlaw", "timid"}
+
+
+def test_interact_step_is_accepted():
+    registry = {}
+    _s, payload, _c = handle_request(
+        "POST", "/session",
+        {"scenario": "errand_runner", "seed": 7, "play_turns": 30}, registry,
+    )
+    sid = payload["session_id"]
+    status, body, _c = handle_request("POST", f"/session/{sid}/act",
+                                      {"action": "interact"}, registry)
+    assert status == 200  # interact is a valid errand_runner action (not a 400)