Rename the Realtime V2 delegation tool and parser constant to
background_agent, and update the tool description and fixtures to match.
Validation: just fmt; cargo check -p codex-api; git diff --check
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Co-authored-by: Codex <noreply@openai.com>
## Stack Position
2/4. Built on top of #14828.
## Base
- #14828
## Unblocks
- #14829
- #14827
## Scope
- Port the realtime v2 wire parsing, session, app-server, and
conversation runtime behavior onto the split websocket-method base.
- Branch runtime behavior directly on the current realtime session kind
instead of parser-derived flow flags.
- Keep regression coverage in the existing e2e suites.
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Co-authored-by: Codex <noreply@openai.com>
- Advertise a `codex` function tool in realtime v2 session updates.
- Emit handoff replies as `function_call_output` items while keeping v1
behavior unchanged.
- Split realtime event parsing into explicit v1/v2 modules with shared
common helpers.
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Co-authored-by: Codex <noreply@openai.com>
- Add a feature-flagged realtime v2 parser on the existing
websocket/session pipeline.
- Wire parser selection from core feature flags and map the codex
handoff tool-call path into existing handoff events.
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Co-authored-by: Codex <noreply@openai.com>
