feat(bot): every free-text message gets the agent's answer; every demo entry is a private copy

- Idle chat: all messages go to the agent (greetings, side-effect and substitute questions included); check-in
  signals are still recorded silently, quit intent keeps its rule reaction. Seen live: «какие будут побочки»
  was logged as a complaint («Спасибо, отметил»), «привет» got a canned phrase.
- Agent prompt: warm short replies to small talk; substitutes → only the doctor changes the drug.
- ЕМИАС demo persona button creates a private copy too (starting from consent + questionnaires, subject to
  the screening switch); the web app drops a stored session of the old shared demo account.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/test_api_patient_web.py

@@ -87,10 +87,14 @@ async def test_emias_rejects_unknown_code(client: AsyncClient) -> None:
 
 async def test_emias_demo_persona(client: AsyncClient) -> None:
     persona = fixtures.DEMO_PERSONAS[0]
-    res = await client.post("/api/v1/auth/emias/demo", json={"persona_token": persona.token})
-    assert res.json() == {"token": persona.token, "mode": "emias", "display_name": persona.display_name}
+    res = (await client.post("/api/v1/auth/emias/demo", json={"persona_token": persona.token})).json()
+    # Every visitor gets a private copy of the persona, never the shared account.
+    assert res["token"].startswith(persona.token + "-") and res["mode"] == "emias"
+    assert res["display_name"] == persona.display_name
+    again = (await client.post("/api/v1/auth/emias/demo", json={"persona_token": persona.token})).json()
+    assert again["token"] != res["token"]
     async with session.get_clinical_session() as s:
-        assert (await repo.get_profile(s, persona.token)).doctor_id == fixtures.DOCTOR_ID
+        assert (await repo.get_profile(s, res["token"])).doctor_id == fixtures.DOCTOR_ID
     missing = await client.post("/api/v1/auth/emias/demo", json={"persona_token": "tok-nobody"})
     assert missing.status_code == 404
 
@@ -141,8 +145,8 @@ async def test_today_links_prescription_to_reference_and_therapy_day(client: Asy
 
 
 async def test_demo_persona_week_mirrors_dashboard_story(client: AsyncClient) -> None:
-    persona = fixtures.DEMO_PERSONAS[0].token
-    await client.post("/api/v1/auth/emias/demo", json={"persona_token": persona})
+    auth = await client.post("/api/v1/auth/emias/demo", json={"persona_token": fixtures.DEMO_PERSONAS[0].token})
+    persona = auth.json()["token"]
     rx = (await client.get(f"/api/v1/me/{persona}/today")).json()["prescriptions"][0]
     assert rx["ref_id"] == "sertraline" and rx["therapy_day"] > 1
 
@@ -159,8 +163,8 @@ async def test_questionnaires_are_off_without_release_or_demo_flag(
 
 async def test_demo_flag_opens_intake_in_the_engine(client: AsyncClient, monkeypatch: pytest.MonkeyPatch) -> None:
     monkeypatch.setenv("INTAKE_DEMO", "1")
-    persona = fixtures.DEMO_PERSONAS[0].token
-    await client.post("/api/v1/auth/emias/demo", json={"persona_token": persona})
+    auth = await client.post("/api/v1/auth/emias/demo", json={"persona_token": fixtures.DEMO_PERSONAS[0].token})
+    persona = auth.json()["token"]
 
     async def press(button: str | None = None) -> list[str]:
         event = {"type": "button", "button": button} if button else {"type": "start"}