Resolve saved Daybreak choices for each subagent turn (#60773)

## Why

A subagent can use a different model from its parent, with different supported access programs. Saved Daybreak choices need to resolve against the subagent's model and remain consistent throughout its turn, including compaction.

## What changed

- Resolve saved choices before native subagent turns start, preserving explicit turn overrides and applying saved toggles on later turns.
- Distinguish inherited parent programs from explicit child selections. Adapt inherited Daybreak Blue/Red selections to the child model while retaining the saved choice as the default for later turns and nested subagents.
- Validate the account associated with automatic selections and reject incompatible saved choices before sending model requests, while retaining rejected user input in conversation history.
- Require model changes to wait until the next turn when a saved Daybreak choice is present.

## Testing

Add coverage for both multi-agent spawn versions, model-specific selection, automatic compaction, WebSocket response reuse, account changes, unsupported choices, and rejected-input persistence across resume.

GitOrigin-RevId: 11971138d656600d9878187225e4d33217e68ad4

codex-rs/core/src/lib.rs

@@ -81,6 +81,7 @@ pub use agent::types::MessageDeliveryMode;
 pub use agent::types::ResolvedMultiAgentV2UsageHints;
 pub use agent::types::SpawnAgentForkMode;
 pub use agent::types::SpawnAgentOptions;
+pub use agent::types::SpawnProgramSource;
 pub use rollout_budget::RolloutBudgetReminder;
 mod agent_communication;
 pub use agent_communication::PendingAgentMessage;