fix(cliproxy): use backend-aware labels in error messages and API

- Use checkCliproxyUpdate() in checkLatestVersion() for correct repo
- Dynamic error messages based on backend in service-manager
- Dynamic error messages based on backend in cliproxy-executor
- Generic "CLIProxy" message in oauth-process (no backend context)

src/cliproxy/services/binary-service.ts

@@ -75,7 +75,10 @@ export async function checkLatestVersion(backend?: CLIProxyBackend): Promise<Lat
     backend ?? loadOrCreateUnifiedConfig().cliproxy?.backend ?? DEFAULT_BACKEND;
 
   try {
-    const latestVersion = await fetchLatestCliproxyVersion();
+    // Use checkCliproxyUpdate which is backend-aware (uses correct GitHub repo)
+    const { checkCliproxyUpdate } = await import('../binary-manager');
+    const updateResult = await checkCliproxyUpdate();
+    const latestVersion = updateResult.latestVersion;
     const currentVersion = getInstalledCliproxyVersion(effectiveBackend);
     const updateAvailable = latestVersion !== currentVersion;