[codex] Defer fork context injection until first turn (#15699)

## Summary
- remove the fork-startup `build_initial_context` injection
- keep the reconstructed `reference_context_item` as the fork baseline
until the first real turn
- update fork-history tests and the request snapshot, and add a
`TODO(ccunningham)` for remaining nondiffable initial-context inputs

## Why
Fork startup was appending current-session initial context immediately
after reconstructing the parent rollout, then the first real turn could
emit context updates again. That duplicated model-visible context in the
child rollout.

## Impact
Forked sessions now behave like resume for context seeding: startup
reconstructs history and preserves the prior baseline, and the first
real turn handles any current-session context emission.

---------

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

codex-rs/core/src/codex.rs

@@ -2215,15 +2215,6 @@ impl Session {
                     self.persist_rollout_items(&rollout_items).await;
                 }
 
-                // Append the current session's initial context after the reconstructed history.
-                let initial_context = self.build_initial_context(&turn_context).await;
-                self.record_conversation_items(&turn_context, &initial_context)
-                    .await;
-                {
-                    let mut state = self.state.lock().await;
-                    state.set_reference_context_item(Some(turn_context.to_turn_context_item()));
-                }
-
                 // Forked threads should remain file-backed immediately after startup.
                 self.ensure_rollout_materialized().await;