feat(app-server): propagate app-server trace context into core

[owenlin0]

Summary

Propagate trace context originating at app-server RPC method handlers -> codex core submission loop (so this includes spans such as run_turn!). This implements PR 2 of the app-server tracing rollout.

This also removes the old lower-level env-based reparenting in core so explicit request/submission ancestry wins instead of being overridden by ambient TRACEPARENT state.

What changed

• Added trace: Option<W3cTraceContext> to codex_protocol::Submission
• Taught Codex::submit() / submit_with_id() to automatically capture the current span context when constructing or forwarding a submission
• Wrapped the core submission loop in a submission_dispatch span parented from Submission.trace
• Warn on invalid submission trace carriers and ignore them cleanly
• Removed the old env-based downstream reparenting path in core task execution
• Stopped OTEL provider init from implicitly attaching env trace context process-wide
• Updated mcp-server Submission call sites for the new field

Added focused unit tests for:

• capturing trace context into Submission
• preferring Submission.trace when building the core dispatch span

Why

PR 1 gave us consistent inbound request spans in app-server, but that only covered the transport boundary. For long-running work like turns and reviews, the important missing piece was preserving ancestry after the request handler returns and core continues work on a different async path.

This change makes that handoff explicit and keeps the parentage rules simple:

• app-server request span sets the current context
• Submission.trace snapshots that context
• core restores it once, at the submission boundary
• deeper core spans inherit naturally

That also lets us stop relying on env-based reparenting for this path, which was too ambient and could override explicit ancestry.

[owenlin0]

@codex review

[chatgpt-codex-connector]

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Reviewed commit: 90585ec15e

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[owenlin0]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Already looking forward to the next diff.

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".