Extract realtime input task handlers (#17280)

Refactor the realtime input task select loop into named handlers for
user text, background agent output, realtime server events, and user
audio without changing the V2 behavior.

Stack:
- Depends on #17278 for the background_agent rename.

Validation:
- just fmt
- cargo check -p codex-core
- git diff --check

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Co-authored-by: Codex <noreply@openai.com>