[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/snapshots/codex_core__codex_tests__fork_startup_context_then_first_turn_diff.snap

@@ -1,17 +1,15 @@
 ---
 source: core/src/codex_tests.rs
-assertion_line: 1282
+assertion_line: 1254
 expression: snapshot
 ---
-Scenario: First request after fork when fork startup changes approval policy and the first forked turn changes approval policy again and enters plan mode.
+Scenario: First request after fork when startup preserves the parent baseline, the fork changes approval policy, and the first forked turn enters plan mode.
 
 ## First Forked Turn Request
 00:message/developer:<PERMISSIONS_INSTRUCTIONS>
 01:message/user:<ENVIRONMENT_CONTEXT:cwd=<CWD>>
 02:message/user:fork seed
-03:message/developer:<PERMISSIONS_INSTRUCTIONS>
-04:message/user:<ENVIRONMENT_CONTEXT:cwd=<CWD>>
-05:message/developer[2]:
+03:message/developer[2]:
     [01] <PERMISSIONS_INSTRUCTIONS>
     [02] <collaboration_mode>Fork turn collaboration instructions.</collaboration_mode>
-06:message/user:after fork
+04:message/user:after fork