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/core/tests/responses_headers.rs

@@ -7,7 +7,7 @@ use codex_core::ModelProviderInfo;
 use codex_core::Prompt;
 use codex_core::ResponseEvent;
 use codex_core::WireApi;
-use codex_otel::OtelManager;
+use codex_otel::SessionTelemetry;
 use codex_otel::TelemetryAuthMode;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::ReasoningSummary;
@@ -72,7 +72,7 @@ async fn responses_stream_includes_subagent_header_on_review() {
     let session_source = SessionSource::SubAgent(SubAgentSource::Review);
     let model_info =
         codex_core::test_support::construct_model_info_offline(model.as_str(), &config);
-    let otel_manager = OtelManager::new(
+    let session_telemetry = SessionTelemetry::new(
         conversation_id,
         model.as_str(),
         model_info.slug.as_str(),
@@ -113,7 +113,7 @@ async fn responses_stream_includes_subagent_header_on_review() {
         .stream(
             &prompt,
             &model_info,
-            &otel_manager,
+            &session_telemetry,
             effort,
             summary.unwrap_or(model_info.default_reasoning_summary),
             None,
@@ -185,7 +185,7 @@ async fn responses_stream_includes_subagent_header_on_other() {
     let model_info =
         codex_core::test_support::construct_model_info_offline(model.as_str(), &config);
 
-    let otel_manager = OtelManager::new(
+    let session_telemetry = SessionTelemetry::new(
         conversation_id,
         model.as_str(),
         model_info.slug.as_str(),
@@ -226,7 +226,7 @@ async fn responses_stream_includes_subagent_header_on_other() {
         .stream(
             &prompt,
             &model_info,
-            &otel_manager,
+            &session_telemetry,
             effort,
             summary.unwrap_or(model_info.default_reasoning_summary),
             None,
@@ -297,7 +297,7 @@ async fn responses_respects_model_info_overrides_from_config() {
         SessionSource::SubAgent(SubAgentSource::Other("override-check".to_string()));
     let model_info =
         codex_core::test_support::construct_model_info_offline(model.as_str(), &config);
-    let otel_manager = OtelManager::new(
+    let session_telemetry = SessionTelemetry::new(
         conversation_id,
         model.as_str(),
         model_info.slug.as_str(),
@@ -338,7 +338,7 @@ async fn responses_respects_model_info_overrides_from_config() {
         .stream(
             &prompt,
             &model_info,
-            &otel_manager,
+            &session_telemetry,
             effort,
             summary.unwrap_or(model_info.default_reasoning_summary),
             None,