fix(providers): thread the session effort knob to Gemini

_GOOGLE_DEFAULT declared no reasoning_effort_values, so
resolve_reasoning_effort returned None and the session effort knob was
silently dropped for every Gemini model — the same bug class this
branch fixed on the local lanes. Gemini's OpenAI-compat surface
documents a flat reasoning_effort (2.5: thinking_budget mapping; 3.x:
thinking_level), so declaring values lights up the inherited
chat-completions path.

Values are the safe cross-model set (minimal/low/medium/high): "none"
is excluded because 2.5 Pro and the 3.x family reject disabling
thinking — and the resolver never forwards the knob's none anyway (the
param is omitted, server default applies). Off-list xhigh/max snap to
the declared default high. Encoded from the official compatibility
docs per the static-caps pattern; not live-verified.

tests/test_providers.py

@@ -1802,6 +1802,39 @@ class TestProviderFactory:
 # ===========================================================================
 
 
+class TestGoogleEffortKnob:
+    """The session effort knob reaches Gemini as a flat reasoning_effort."""
+
+    def _create_kwargs(self, reasoning_effort: str) -> dict[str, Any]:
+        from turnstone.core.providers._google import GoogleProvider
+
+        prov = GoogleProvider()
+        client = MagicMock()
+        client.chat.completions.create.return_value = iter([])
+        list(
+            prov.create_streaming(
+                client=client,
+                model="gemini-3-flash",
+                messages=[{"role": "user", "content": "hi"}],
+                reasoning_effort=reasoning_effort,
+            )
+        )
+        return client.chat.completions.create.call_args[1]
+
+    def test_knob_values_forward_verbatim(self) -> None:
+        for knob in ("minimal", "low", "medium", "high"):
+            assert self._create_kwargs(knob)["reasoning_effort"] == knob
+
+    def test_off_list_knob_snaps_to_high(self) -> None:
+        """xhigh/max are not in Gemini's vocabulary — snap down to high."""
+        for knob in ("xhigh", "max"):
+            assert self._create_kwargs(knob)["reasoning_effort"] == "high"
+
+    def test_none_omits_the_param(self) -> None:
+        """Knob none never sends "none" — 2.5 Pro / 3.x reject disabling."""
+        assert "reasoning_effort" not in self._create_kwargs("none")
+
+
 class TestGoogleProviderFidelity:
     """Tests for thought_signature round-trip via provider_blocks."""
 

turnstone/core/providers/_google.py

@@ -43,6 +43,19 @@ _GOOGLE_DEFAULT = ModelCapabilities(
     # Gemini's OpenAI-compat endpoint accepts max_tokens (not
     # max_completion_tokens which is OpenAI Responses-specific).
     token_param="max_tokens",
+    # Gemini's OpenAI-compat endpoint accepts a flat ``reasoning_effort``
+    # (2.5 family: thinking_budget 1024/1024/8192/24576 for minimal/low/
+    # medium/high; 3.x family: thinking_level of the same name).  The
+    # declared values are the safe set across ALL current Gemini models:
+    # "none" is excluded because 2.5 Pro and the 3.x family reject
+    # disabling thinking — and ``resolve_reasoning_effort`` never
+    # forwards the knob's "none" anyway (the param is omitted and the
+    # server default applies).  Off-list knob values (xhigh, max) snap
+    # to the default "high".  Encoded from
+    # ai.google.dev/gemini-api/docs/openai (2026-07); not live-verified —
+    # the static-caps pattern for commercial providers.
+    reasoning_effort_values=("minimal", "low", "medium", "high"),
+    default_reasoning_effort="high",
 )