chore(otel): rename OtelManager to SessionTelemetry (#13808)

## Summary
This is a purely mechanical refactor of `OtelManager` ->
`SessionTelemetry` to better convey what the struct is doing. No
behavior change.

## Why

`OtelManager` ended up sounding much broader than what this type
actually does. It doesn't manage OTEL globally; it's the session-scoped
telemetry surface for emitting log/trace events and recording metrics
with consistent session metadata (`app_version`, `model`, `slug`,
`originator`, etc.).

`SessionTelemetry` is a more accurate name, and updating the call sites
makes that boundary a lot easier to follow.

## Validation

- `just fmt`
- `cargo test -p codex-otel`
- `cargo test -p codex-core`

codex-rs/otel/tests/suite/manager_metrics.rs

@@ -2,7 +2,7 @@ use crate::harness::attributes_to_map;
 use crate::harness::build_metrics_with_defaults;
 use crate::harness::find_metric;
 use crate::harness::latest_metrics;
-use codex_otel::OtelManager;
+use codex_otel::SessionTelemetry;
 use codex_otel::TelemetryAuthMode;
 use codex_otel::metrics::Result;
 use codex_protocol::ThreadId;
@@ -12,11 +12,11 @@ use opentelemetry_sdk::metrics::data::MetricData;
 use pretty_assertions::assert_eq;
 use std::collections::BTreeMap;
 
-// Ensures OtelManager attaches metadata tags when forwarding metrics.
+// Ensures SessionTelemetry attaches metadata tags when forwarding metrics.
 #[test]
 fn manager_attaches_metadata_tags_to_metrics() -> Result<()> {
     let (metrics, exporter) = build_metrics_with_defaults(&[("service", "codex-cli")])?;
-    let manager = OtelManager::new(
+    let manager = SessionTelemetry::new(
         ThreadId::new(),
         "gpt-5.1",
         "gpt-5.1",
@@ -68,11 +68,11 @@ fn manager_attaches_metadata_tags_to_metrics() -> Result<()> {
     Ok(())
 }
 
-// Ensures metadata tagging can be disabled when recording via OtelManager.
+// Ensures metadata tagging can be disabled when recording via SessionTelemetry.
 #[test]
 fn manager_allows_disabling_metadata_tags() -> Result<()> {
     let (metrics, exporter) = build_metrics_with_defaults(&[])?;
-    let manager = OtelManager::new(
+    let manager = SessionTelemetry::new(
         ThreadId::new(),
         "gpt-4o",
         "gpt-4o",
@@ -113,7 +113,7 @@ fn manager_allows_disabling_metadata_tags() -> Result<()> {
 #[test]
 fn manager_attaches_optional_service_name_tag() -> Result<()> {
     let (metrics, exporter) = build_metrics_with_defaults(&[])?;
-    let manager = OtelManager::new(
+    let manager = SessionTelemetry::new(
         ThreadId::new(),
         "gpt-5.1",
         "gpt-5.1",

codex-rs/otel/tests/suite/otel_export_routing_policy.rs

@@ -1,4 +1,4 @@
-use codex_otel::OtelManager;
+use codex_otel::SessionTelemetry;
 use codex_otel::TelemetryAuthMode;
 use codex_otel::otel_provider::OtelProvider;
 use opentelemetry::KeyValue;
@@ -103,7 +103,7 @@ fn otel_export_routing_policy_routes_user_prompt_log_and_trace_events() {
 
     tracing::subscriber::with_default(subscriber, || {
         tracing::callsite::rebuild_interest_cache();
-        let manager = OtelManager::new(
+        let manager = SessionTelemetry::new(
             ThreadId::new(),
             "gpt-5.1",
             "gpt-5.1",
@@ -212,7 +212,7 @@ fn otel_export_routing_policy_routes_tool_result_log_and_trace_events() {
 
     tracing::subscriber::with_default(subscriber, || {
         tracing::callsite::rebuild_interest_cache();
-        let manager = OtelManager::new(
+        let manager = SessionTelemetry::new(
             ThreadId::new(),
             "gpt-5.1",
             "gpt-5.1",

codex-rs/otel/tests/suite/runtime_summary.rs

@@ -1,6 +1,6 @@
-use codex_otel::OtelManager;
 use codex_otel::RuntimeMetricTotals;
 use codex_otel::RuntimeMetricsSummary;
+use codex_otel::SessionTelemetry;
 use codex_otel::TelemetryAuthMode;
 use codex_otel::metrics::MetricsClient;
 use codex_otel::metrics::MetricsConfig;
@@ -20,7 +20,7 @@ fn runtime_metrics_summary_collects_tool_api_and_streaming_metrics() -> Result<(
         MetricsConfig::in_memory("test", "codex-cli", env!("CARGO_PKG_VERSION"), exporter)
             .with_runtime_reader(),
     )?;
-    let manager = OtelManager::new(
+    let manager = SessionTelemetry::new(
         ThreadId::new(),
         "gpt-5.1",
         "gpt-5.1",

codex-rs/otel/tests/suite/snapshot.rs

@@ -1,6 +1,6 @@
 use crate::harness::attributes_to_map;
 use crate::harness::find_metric;
-use codex_otel::OtelManager;
+use codex_otel::SessionTelemetry;
 use codex_otel::TelemetryAuthMode;
 use codex_otel::metrics::MetricsClient;
 use codex_otel::metrics::MetricsConfig;
@@ -69,7 +69,7 @@ fn manager_snapshot_metrics_collects_without_shutdown() -> Result<()> {
         .with_tag("service", "codex-cli")?
         .with_runtime_reader();
     let metrics = MetricsClient::new(config)?;
-    let manager = OtelManager::new(
+    let manager = SessionTelemetry::new(
         ThreadId::new(),
         "gpt-5.1",
         "gpt-5.1",