fix: separate Telegram connection pools and add timeout retry to prevent pool exhaustion

The root cause of "Pool timeout" errors is that long-polling (getUpdates)
and outbound API calls (send_message, send_photo, etc.) shared the same
HTTPXRequest pool — polling holds connections indefinitely, starving sends
under concurrent load (e.g. cron jobs + user chat).

- Split into two independent pools: API calls (default 32) and polling (4)
- Expose connection_pool_size / pool_timeout in TelegramConfig for tuning
- Add _call_with_retry() with exponential backoff (3 attempts) on TimedOut
- Apply retry to _send_text and remote media URL sends

tests/test_telegram_channel.py

@@ -18,6 +18,10 @@ class _FakeHTTPXRequest:
         self.kwargs = kwargs
         self.__class__.instances.append(self)
 
+    @classmethod
+    def clear(cls) -> None:
+        cls.instances.clear()
+
 
 class _FakeUpdater:
     def __init__(self, on_start_polling) -> None:
@@ -144,7 +148,8 @@ def _make_telegram_update(
 
 
 @pytest.mark.asyncio
-async def test_start_uses_request_proxy_without_builder_proxy(monkeypatch) -> None:
+async def test_start_creates_separate_pools_with_proxy(monkeypatch) -> None:
+    _FakeHTTPXRequest.clear()
     config = TelegramConfig(
         enabled=True,
         token="123:abc",
@@ -164,10 +169,106 @@ async def test_start_uses_request_proxy_without_builder_proxy(monkeypatch) -> No
 
     await channel.start()
 
-    assert len(_FakeHTTPXRequest.instances) == 1
-    assert _FakeHTTPXRequest.instances[0].kwargs["proxy"] == config.proxy
-    assert builder.request_value is _FakeHTTPXRequest.instances[0]
-    assert builder.get_updates_request_value is _FakeHTTPXRequest.instances[0]
+    assert len(_FakeHTTPXRequest.instances) == 2
+    api_req, poll_req = _FakeHTTPXRequest.instances
+    assert api_req.kwargs["proxy"] == config.proxy
+    assert poll_req.kwargs["proxy"] == config.proxy
+    assert api_req.kwargs["connection_pool_size"] == 32
+    assert poll_req.kwargs["connection_pool_size"] == 4
+    assert builder.request_value is api_req
+    assert builder.get_updates_request_value is poll_req
+
+
+@pytest.mark.asyncio
+async def test_start_respects_custom_pool_config(monkeypatch) -> None:
+    _FakeHTTPXRequest.clear()
+    config = TelegramConfig(
+        enabled=True,
+        token="123:abc",
+        allow_from=["*"],
+        connection_pool_size=32,
+        pool_timeout=10.0,
+    )
+    bus = MessageBus()
+    channel = TelegramChannel(config, bus)
+    app = _FakeApp(lambda: setattr(channel, "_running", False))
+    builder = _FakeBuilder(app)
+
+    monkeypatch.setattr("nanobot.channels.telegram.HTTPXRequest", _FakeHTTPXRequest)
+    monkeypatch.setattr(
+        "nanobot.channels.telegram.Application",
+        SimpleNamespace(builder=lambda: builder),
+    )
+
+    await channel.start()
+
+    api_req = _FakeHTTPXRequest.instances[0]
+    poll_req = _FakeHTTPXRequest.instances[1]
+    assert api_req.kwargs["connection_pool_size"] == 32
+    assert api_req.kwargs["pool_timeout"] == 10.0
+    assert poll_req.kwargs["pool_timeout"] == 10.0
+
+
+@pytest.mark.asyncio
+async def test_send_text_retries_on_timeout() -> None:
+    """_send_text retries on TimedOut before succeeding."""
+    from telegram.error import TimedOut
+
+    channel = TelegramChannel(
+        TelegramConfig(enabled=True, token="123:abc", allow_from=["*"]),
+        MessageBus(),
+    )
+    channel._app = _FakeApp(lambda: None)
+
+    call_count = 0
+    original_send = channel._app.bot.send_message
+
+    async def flaky_send(**kwargs):
+        nonlocal call_count
+        call_count += 1
+        if call_count <= 2:
+            raise TimedOut()
+        return await original_send(**kwargs)
+
+    channel._app.bot.send_message = flaky_send
+
+    import nanobot.channels.telegram as tg_mod
+    orig_delay = tg_mod._SEND_RETRY_BASE_DELAY
+    tg_mod._SEND_RETRY_BASE_DELAY = 0.01
+    try:
+        await channel._send_text(123, "hello", None, {})
+    finally:
+        tg_mod._SEND_RETRY_BASE_DELAY = orig_delay
+
+    assert call_count == 3
+    assert len(channel._app.bot.sent_messages) == 1
+
+
+@pytest.mark.asyncio
+async def test_send_text_gives_up_after_max_retries() -> None:
+    """_send_text raises TimedOut after exhausting all retries."""
+    from telegram.error import TimedOut
+
+    channel = TelegramChannel(
+        TelegramConfig(enabled=True, token="123:abc", allow_from=["*"]),
+        MessageBus(),
+    )
+    channel._app = _FakeApp(lambda: None)
+
+    async def always_timeout(**kwargs):
+        raise TimedOut()
+
+    channel._app.bot.send_message = always_timeout
+
+    import nanobot.channels.telegram as tg_mod
+    orig_delay = tg_mod._SEND_RETRY_BASE_DELAY
+    tg_mod._SEND_RETRY_BASE_DELAY = 0.01
+    try:
+        await channel._send_text(123, "hello", None, {})
+    finally:
+        tg_mod._SEND_RETRY_BASE_DELAY = orig_delay
+
+    assert channel._app.bot.sent_messages == []
 
 
 def test_derive_topic_session_key_uses_thread_id() -> None: