fix: split HTTP connect/read timeouts (Jellyfin build + qBit stats)

Every HTTP client passed an integer timeout to requests, applying the same
value to BOTH connect and read phases. A slow Jellyfin /Items page or qBit
/sync/maindata blew through the 10s read budget → ReadTimeoutError. Split
into a (connect=5s, read=60s default) tuple via shared http_timeout() helper.
The media index build worker uses a 180s read floor. Existing services with
low timeout_seconds benefit from bumping to 60+.

backend/tests/test_http_timeout.py

@@ -0,0 +1,39 @@
+"""Tests for the shared HTTP timeout helper."""
+
+from __future__ import annotations
+
+from media_library_viewer_api.clients.http_timeout import (
+    DEFAULT_CONNECT_TIMEOUT,
+    DEFAULT_READ_TIMEOUT,
+    http_timeout,
+)
+
+
+class TestHttpTimeout:
+    def test_http_timeout_returns_tuple(self) -> None:
+        result = http_timeout(30)
+        assert result == (DEFAULT_CONNECT_TIMEOUT, 30.0)
+
+    def test_http_timeout_default_when_none(self) -> None:
+        result = http_timeout(None)
+        assert result == (DEFAULT_CONNECT_TIMEOUT, DEFAULT_READ_TIMEOUT)
+
+    def test_http_timeout_default_when_zero(self) -> None:
+        result = http_timeout(0)
+        assert result == (DEFAULT_CONNECT_TIMEOUT, DEFAULT_READ_TIMEOUT)
+
+    def test_http_timeout_custom_connect(self) -> None:
+        result = http_timeout(30, connect_timeout=10)
+        assert result == (10.0, 30.0)
+
+    def test_http_timeout_default_when_negative(self) -> None:
+        result = http_timeout(-5)
+        assert result == (DEFAULT_CONNECT_TIMEOUT, DEFAULT_READ_TIMEOUT)
+
+    def test_http_timeout_default_when_garbage_string(self) -> None:
+        result = http_timeout("garbage")  # type: ignore[arg-type]
+        assert result == (DEFAULT_CONNECT_TIMEOUT, DEFAULT_READ_TIMEOUT)
+
+    def test_http_timeout_accepts_int(self) -> None:
+        result = http_timeout(45)
+        assert result == (5.0, 45.0)

backend/tests/test_qbittorrent_client.py

@@ -129,6 +129,21 @@ class QbittorrentClientTests(unittest.TestCase):
         with self.assertRaises(requests.ConnectionError):
             client._login()
 
+    def test_qbittorrent_client_uses_tuple_timeout(self) -> None:
+        """The client passes a (connect, read) tuple to requests, not an int."""
+        # self.client was constructed with timeout=5 in setUp() and has a mocked session.
+        assert isinstance(self.client.timeout, tuple)
+        assert len(self.client.timeout) == 2
+        assert self.client.timeout[0] == 5.0  # connect timeout
+        assert self.client.timeout[1] == 5.0  # read timeout (what we passed)
+
+        # Verify it's actually passed to requests as-is.
+        self.session.post.return_value = self._login_response()
+        self.client._login()
+        call_kwargs = self.session.post.call_args.kwargs
+        assert call_kwargs["timeout"] == (5.0, 5.0)
+        assert not isinstance(call_kwargs["timeout"], int)
+
 
 if __name__ == "__main__":
     unittest.main()