fix(auth): isolate chatgptAuthTokens concept to auth manager and app-server (#10423)

So that the rest of the codebase (like TUI) don't need to be concerned
whether ChatGPT auth was handled by Codex itself or passed in via
app-server's external auth mode.

codex-rs/otel/src/lib.rs

@@ -31,6 +31,13 @@ pub enum ToolDecisionSource {
     User,
 }
 
+/// Maps to core AuthMode to avoid a circular dependency on codex-core.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Display)]
+pub enum TelemetryAuthMode {
+    ApiKey,
+    Chatgpt,
+}
+
 #[derive(Debug, Clone)]
 pub struct OtelEventMetadata {
     pub(crate) conversation_id: ThreadId,

codex-rs/otel/src/traces/otel_manager.rs

@@ -1,3 +1,4 @@
+use crate::TelemetryAuthMode;
 use crate::metrics::names::API_CALL_COUNT_METRIC;
 use crate::metrics::names::API_CALL_DURATION_METRIC;
 use crate::metrics::names::RESPONSES_API_INFERENCE_TIME_DURATION_METRIC;
@@ -15,7 +16,6 @@ use chrono::SecondsFormat;
 use chrono::Utc;
 use codex_api::ApiError;
 use codex_api::ResponseEvent;
-use codex_app_server_protocol::AuthMode;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::ReasoningSummary;
 use codex_protocol::models::ResponseItem;
@@ -57,7 +57,7 @@ impl OtelManager {
         slug: &str,
         account_id: Option<String>,
         account_email: Option<String>,
-        auth_mode: Option<AuthMode>,
+        auth_mode: Option<TelemetryAuthMode>,
         log_user_prompts: bool,
         terminal_type: String,
         session_source: SessionSource,