[codex] Initialize exec-server OpenTelemetry at startup (#25019)

## Summary

- Initialize stderr tracing and the configured OpenTelemetry provider
for local and remote `codex exec-server` startup.
- Instrument the local and remote server entrypoints with a root runtime
span.
- Keep raw Noise environment, registration, and stream identifiers out
of exported spans while preserving them in local debug events.
- Keep telemetry setup in a focused CLI module instead of growing the
top-level command entrypoint.

## Stack

- Previous: none (`#27058` has merged)
- Next: #27466

## Validation

- `just test -p codex-exec-server --lib` (139 passed)
- `just test -p codex-cli --test exec_server` (3 passed)
- `just bazel-lock-check`
- `just fix -p codex-exec-server -p codex-cli`
- `just fmt`

---------

Co-authored-by: Richard Lee <richardlee@openai.com>

codex-rs/cli/src/exec_server_telemetry.rs

@@ -0,0 +1,41 @@
+use tracing_subscriber::EnvFilter;
+use tracing_subscriber::prelude::*;
+
+const DEFAULT_ANALYTICS_ENABLED: bool = false;
+const DEFAULT_LOG_FILTER: &str = "error,opentelemetry_sdk=off,opentelemetry_otlp=off";
+const OTEL_SERVICE_NAME: &str = "codex-exec-server";
+
+pub(crate) fn init(
+    config: Option<&codex_core::config::Config>,
+) -> Result<impl Send + Sync, Box<dyn std::error::Error>> {
+    let fmt_layer = tracing_subscriber::fmt::layer()
+        .with_writer(std::io::stderr)
+        .with_filter(stderr_env_filter());
+    let otel = match config {
+        Some(config) => codex_core::otel_init::build_provider(
+            config,
+            env!("CARGO_PKG_VERSION"),
+            Some(OTEL_SERVICE_NAME),
+            DEFAULT_ANALYTICS_ENABLED,
+        ),
+        None => Ok(None),
+    };
+    let provider = otel.as_ref().ok().and_then(Option::as_ref);
+    codex_core::otel_init::record_process_start(provider, OTEL_SERVICE_NAME);
+
+    let otel_logger_layer = provider.and_then(|otel| otel.logger_layer());
+    let otel_tracing_layer = provider.and_then(|otel| otel.tracing_layer());
+    let _ = tracing_subscriber::registry()
+        .with(fmt_layer)
+        .with(otel_tracing_layer)
+        .with(otel_logger_layer)
+        .try_init();
+    tracing::callsite::rebuild_interest_cache();
+    otel
+}
+
+fn stderr_env_filter() -> EnvFilter {
+    EnvFilter::try_from_default_env()
+        .or_else(|_| EnvFilter::try_new(DEFAULT_LOG_FILTER))
+        .unwrap_or_else(|_| EnvFilter::new("error"))
+}