Support for Background Compaction

What variant of Codex are you using?

App

What feature would you like to see?

Compaction currently pauses the agent loop while the previous context is compacted. Codex could make compaction time completely hidden if the agent is allowed to continue working during this time.

This involves

1. Taking a snapshot of the conversation and sending it to the compaction endpoint.
2. While that happens, the agent should continue working.
3. When the compacted context is ready, it should replace the context up to the snapshot point.

This is already implemented in GH Copilot.

Additional information

_No response_