Logs the auth type in the user prompts, api responses and errors (#3795)

packages/cli/src/gemini.tsx

@@ -212,6 +212,7 @@ export async function main() {
     'event.timestamp': new Date().toISOString(),
     prompt: input,
     prompt_id,
+    auth_type: config.getContentGeneratorConfig().authType!,
     prompt_length: input.length,
   });