feat(providers): add warmup() for OpenAI, Anthropic, Gemini, Compatible, GLM

All five providers have HTTP clients but did not implement warmup(),
relying on the trait default no-op. This adds lightweight warmup calls
to establish TLS + HTTP/2 connection pools on startup, reducing
first-request latency. Each warmup is skipped when credentials are
absent, matching the OpenRouter pattern.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/providers/gemini.rs

@@ -396,6 +396,27 @@ impl Provider for GeminiProvider {
             .and_then(|p| p.text)
             .ok_or_else(|| anyhow::anyhow!("No response from Gemini"))
     }
+
+    async fn warmup(&self) -> anyhow::Result<()> {
+        if let Some(auth) = self.auth.as_ref() {
+            let url = if auth.is_api_key() {
+                format!(
+                    "https://generativelanguage.googleapis.com/v1beta/models?key={}",
+                    auth.credential()
+                )
+            } else {
+                "https://generativelanguage.googleapis.com/v1beta/models".to_string()
+            };
+
+            let mut request = self.client.get(&url);
+            if let GeminiAuth::OAuthToken(token) = auth {
+                request = request.bearer_auth(token);
+            }
+
+            request.send().await?.error_for_status()?;
+        }
+        Ok(())
+    }
 }
 
 #[cfg(test)]
@@ -665,4 +686,11 @@ mod tests {
         assert!(response.error.is_some());
         assert_eq!(response.error.unwrap().message, "Invalid API key");
     }
+
+    #[tokio::test]
+    async fn warmup_without_key_is_noop() {
+        let provider = GeminiProvider::new(None);
+        let result = provider.warmup().await;
+        assert!(result.is_ok());
+    }
 }