Extract codex-analytics crate (#15748)

## Summary
- move the analytics events client into codex-analytics
- update codex-core and app-server callsites to use the new crate

## Testing
- CI

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/app-server/src/config_api.rs

@@ -450,6 +450,8 @@ fn config_write_error(code: ConfigWriteErrorCode, message: impl Into<String>) ->
 mod tests {
     use super::*;
     use codex_core::AnalyticsEventsClient;
+    use codex_core::AuthManager;
+    use codex_core::CodexAuth;
     use codex_core::config_loader::NetworkRequirementsToml as CoreNetworkRequirementsToml;
     use codex_features::Feature;
     use codex_protocol::protocol::AskForApproval as CoreAskForApproval;
@@ -651,6 +653,7 @@ mod tests {
                 .await
                 .expect("load analytics config"),
         );
+        let auth_manager = AuthManager::from_auth_for_testing(CodexAuth::from_api_key("test"));
         let config_api = ConfigApi::new(
             codex_home.path().to_path_buf(),
             Arc::new(RwLock::new(Vec::new())),
@@ -659,10 +662,12 @@ mod tests {
             Arc::new(RwLock::new(CloudRequirementsLoader::default())),
             reloader.clone(),
             AnalyticsEventsClient::new(
-                analytics_config,
-                codex_core::test_support::auth_manager_from_auth(
-                    codex_core::CodexAuth::from_api_key("test"),
-                ),
+                auth_manager,
+                analytics_config
+                    .chatgpt_base_url
+                    .trim_end_matches('/')
+                    .to_string(),
+                analytics_config.analytics_enabled,
             ),
         );