feat(gemini): improve request context for support and compatibility

Include the Hermes client name and version with Gemini inference, model and tier checks, and TTS requests. Add focused coverage for the request headers and keep the Gemini-specific context scoped to Google Gemini endpoints.

tests/hermes_cli/test_model_validation.py

@@ -942,3 +942,33 @@ class TestProbeApiModelsUserAgent:
         assert ua and ua.startswith("hermes-cli/")
         # No Authorization was set, but UA must still be present.
         assert req.get_header("Authorization") is None
+
+    def test_probe_sends_client_context_to_gemini(self):
+        from unittest.mock import patch
+        from hermes_cli.models import _HERMES_VERSION
+
+        body = b'{"data":[]}'
+        with patch(
+            "hermes_cli.models.urllib.request.urlopen",
+            return_value=self._make_mock_response(body),
+        ) as mock_urlopen:
+            probe_api_models(
+                "gemini-key",
+                "https://generativelanguage.googleapis.com/v1beta/openai",
+            )
+
+        req = mock_urlopen.call_args[0][0]
+        assert req.get_header("X-goog-api-client") == f"hermes-agent/{_HERMES_VERSION}"
+
+    def test_probe_omits_gemini_client_context_for_other_providers(self):
+        from unittest.mock import patch
+
+        body = b'{"data":[]}'
+        with patch(
+            "hermes_cli.models.urllib.request.urlopen",
+            return_value=self._make_mock_response(body),
+        ) as mock_urlopen:
+            probe_api_models("provider-key", "https://api.example.com/v1")
+
+        req = mock_urlopen.call_args[0][0]
+        assert req.get_header("X-goog-api-client") is None