feat(dashboard): demo console with web chat, demo clock, scenario playback and split screen

- pages/2_Демо-консоль.py: persona selector, virtual clock bar (+1 h, to 08:00/20:00,
  next day, reset with confirm), fallback patient web chat (buttons from Reply.buttons,
  kind styling, outbox drained after every action and on a 2 s fragment poll), scenario panel
- pages/3_Сплит-экран.py: patient chat or PATIENT_WEB_URL iframe on the left, compact doctor
  panel (patients, live alerts, red banner on a new acute alert) on the right
- console/playback.py: data/synthetic/<persona>.jsonl runner (advance_to/press/text/
  expect_color/start), date chaining between days, pause on failure with retry/skip/manual
- console/api.py: own HTTP client over the frozen API contract, ApiError only

Refs #17

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

dashboard/pages/3_Сплит-экран.py

@@ -0,0 +1,58 @@
+"""Split screen for the projector (#17): patient on the left, doctor on the right, clock on top.
+
+Left: the patient web app in an iframe when `PATIENT_WEB_URL` is set (React app, e.g. http://localhost:5173),
+otherwise the console's fallback web chat. Right: compact doctor panel polled every 2 s with a red banner
+on a new acute alert.
+"""
+
+import sys
+from pathlib import Path
+
+import streamlit as st
+
+# `streamlit run dashboard/app.py` already puts dashboard/ on sys.path; this keeps the page runnable on its own.
+sys.path.insert(0, str(Path(__file__).resolve().parents[1]))
+
+from console import widgets as w  # noqa: E402
+
+st.set_page_config(page_title="Сплит-экран", page_icon="🖥️", layout="wide", initial_sidebar_state="collapsed")
+st.markdown(
+    "<style>.block-container{padding-top:1.2rem;max-width:100%} "
+    "[data-testid='stMarkdownContainer'] p, [data-testid='stMarkdownContainer'] li{font-size:1.08rem}</style>",
+    unsafe_allow_html=True,
+)
+
+persona = w.select_persona()
+w.show_flash()
+token = persona["token"]
+
+top, play = st.columns([6, 1.3], vertical_alignment="center")
+with top:
+    w.render_clock_bar(persona, key="split-clock", with_reset=False)
+with play:
+    scenario, _ = w.scenario_for(persona)
+    runner = w.make_runner(persona, delay=0.8)
+    nxt = runner.next_day(scenario) if scenario.days else None
+    clicked = st.button(
+        f"▶ Сценарий: день {nxt.day}" if nxt else "Сценарий проигран",
+        disabled=nxt is None,
+        width="stretch",
+        help="Проиграть следующий день из data/synthetic/<персона>.jsonl",
+    )
+if clicked and nxt is not None:
+    w.execute(runner.play_day(scenario, nxt.day), w.playback_state(token), title=f"День {nxt.day}")
+    st.rerun()
+
+left, right = st.columns([1.1, 1], gap="large")
+with left:
+    url = w.patient_web_url()
+    if url:
+        st.markdown(f"#### 📱 Пациент — {persona.get('display_name') or token}")
+        st.iframe(url, height=760)
+        st.caption(f"Веб-приложение пациента: {url}")
+    else:
+        st.markdown(f"#### 💬 Пациент — {persona.get('display_name') or token}")
+        w.render_chat(token, height=600, key="split-chat")
+with right:
+    st.markdown("#### 🩺 Кабинет врача — д-р Смирнова Е. А.")
+    w.polled_doctor_panel(token, key="split-doc")