chore(otel): reorganize codex-otel crate (#13800)

## Summary
This is a structural cleanup of `codex-otel` to make the ownership
boundaries a lot clearer.

For example, previously it was quite confusing that `OtelManager` which
emits log + trace event telemetry lived under
`codex-rs/otel/src/traces/`. Also, there were two places that defined
methods on OtelManager via `impl OtelManager` (`lib.rs` and
`otel_manager.rs`).

What changed:
- move the `OtelProvider` implementation into `src/provider.rs`
- move `OtelManager` and session-scoped event emission into
`src/events/otel_manager.rs`
- collapse the shared log/trace event helpers into
`src/events/shared.rs`
- pull target classification into `src/targets.rs`
- move `traceparent_context_from_env()` into `src/trace_context.rs`
- keep `src/otel_provider.rs` as a compatibility shim for existing
imports
- update the `codex-otel` README to reflect the new layout

## Why
`lib.rs` and `otel_provider.rs` were doing too many different jobs at
once: provider setup, export routing, trace-context helpers, and session
event emission all lived together.

This refactor separates those concerns without trying to change the
behavior of the crate. The goal is to make future OTEL work easier to
reason about and easier to review.

## Notes
- no intended behavior change
- `OtelManager` remains the session-scoped event emitter in this PR
- the `otel_provider` shim keeps downstream churn low while the
internals move around

## Validation
- `just fmt`
- `cargo test -p codex-otel`
- `just fix -p codex-otel`

codex-rs/otel/src/trace_context.rs

@@ -1,4 +1,6 @@
 use std::collections::HashMap;
+use std::env;
+use std::sync::OnceLock;
 
 use codex_protocol::protocol::W3cTraceContext;
 use opentelemetry::Context;
@@ -6,8 +8,14 @@ use opentelemetry::propagation::TextMapPropagator;
 use opentelemetry::trace::TraceContextExt;
 use opentelemetry_sdk::propagation::TraceContextPropagator;
 use tracing::Span;
+use tracing::debug;
+use tracing::warn;
 use tracing_opentelemetry::OpenTelemetrySpanExt;
 
+const TRACEPARENT_ENV_VAR: &str = "TRACEPARENT";
+const TRACESTATE_ENV_VAR: &str = "TRACESTATE";
+static TRACEPARENT_CONTEXT: OnceLock<Option<Context>> = OnceLock::new();
+
 pub fn current_span_w3c_trace_context() -> Option<W3cTraceContext> {
     let context = Span::current().context();
     if !context.span().span_context().is_valid() {
@@ -51,6 +59,12 @@ pub fn set_parent_from_context(span: &Span, context: Context) {
     let _ = span.set_parent(context);
 }
 
+pub fn traceparent_context_from_env() -> Option<Context> {
+    TRACEPARENT_CONTEXT
+        .get_or_init(load_traceparent_context)
+        .clone()
+}
+
 pub(crate) fn context_from_trace_headers(
     traceparent: Option<&str>,
     tracestate: Option<&str>,
@@ -69,6 +83,22 @@ pub(crate) fn context_from_trace_headers(
     Some(context)
 }
 
+fn load_traceparent_context() -> Option<Context> {
+    let traceparent = env::var(TRACEPARENT_ENV_VAR).ok()?;
+    let tracestate = env::var(TRACESTATE_ENV_VAR).ok();
+
+    match context_from_trace_headers(Some(&traceparent), tracestate.as_deref()) {
+        Some(context) => {
+            debug!("TRACEPARENT detected; continuing trace from parent context");
+            Some(context)
+        }
+        None => {
+            warn!("TRACEPARENT is set but invalid; ignoring trace context");
+            None
+        }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::context_from_trace_headers;