fix(telegram): retry on httpx pool timeout instead of dropping the send (#35664)

When PTB's general httpx pool is exhausted, it converts httpx.PoolTimeout
into telegram.error.TimedOut whose message states the request was *not*
sent to Telegram. The send retry loop treated all non-connect TimedOut as
non-retryable, so a pool timeout raised immediately, skipped all 3 retry
attempts, and was returned as retryable=False -- silently dropping the
message (agent responses, cron reports, etc.).

A pool timeout means the request never left the process, making it the
safest case to retry. Add _looks_like_pool_timeout() and treat it like a
connect timeout in both the in-loop retry decision and the outer retryable
determination, so pool timeouts flow through the existing backoff loop and
stay retryable on exhaustion.

Reported-by: q3874758 (#35610)

tests/gateway/test_telegram_thread_fallback.py

@@ -1278,6 +1278,60 @@ async def test_send_marks_wrapped_connect_timeout_retryable_after_exhaustion():
     assert attempt[0] == 3
 
 
+@pytest.mark.asyncio
+async def test_send_retries_pool_timeout():
+    """Retry TimedOut when it is an httpx pool-timeout (request not sent).
+
+    PTB wraps ``httpx.PoolTimeout`` into ``TimedOut`` with a message that
+    explicitly states the request was *not* sent to Telegram. Re-sending is
+    safe and prevents a silent drop when the pool frees up.
+    """
+    adapter = _make_adapter()
+
+    attempt = [0]
+
+    async def mock_send_message(**kwargs):
+        attempt[0] += 1
+        if attempt[0] < 3:
+            raise FakeTimedOut(
+                "Pool timeout: All connections in the connection pool are "
+                "occupied. Request was *not* sent to Telegram. Consider "
+                "adjusting the connection pool size or the pool timeout."
+            )
+        return SimpleNamespace(message_id=202)
+
+    adapter._bot = SimpleNamespace(send_message=mock_send_message)
+
+    result = await adapter.send(chat_id="123", content="test message")
+
+    assert result.success is True
+    assert result.message_id == "202"
+    assert attempt[0] == 3
+
+
+@pytest.mark.asyncio
+async def test_send_marks_pool_timeout_retryable_after_exhaustion():
+    """Pool timeout that never clears stays retryable for outer retry handling."""
+    adapter = _make_adapter()
+
+    attempt = [0]
+
+    async def mock_send_message(**kwargs):
+        attempt[0] += 1
+        raise FakeTimedOut(
+            "Pool timeout: All connections in the connection pool are occupied. "
+            "Request was *not* sent to Telegram."
+        )
+
+    adapter._bot = SimpleNamespace(send_message=mock_send_message)
+
+    result = await adapter.send(chat_id="123", content="test message")
+
+    assert result.success is False
+    assert result.retryable is True
+    assert attempt[0] == 3
+
+
 @pytest.mark.asyncio
 async def test_thread_fallback_only_fires_once():
     """After clearing thread_id, subsequent chunks should also use None."""