Bug: Flaky tests left ignored without resolution

Description

Multiple tests are marked #[ignore] with flaky-related TODO comments. These represent real functionality that is not being verified in CI:

1. codex-rs/core/tests/suite/pending_input.rs:221 — injected_user_input_triggers_follow_up_request_with_deltas

``
#[ignore = "TODO(aibrahim): flaky"]
``

1. codex-rs/app-server/tests/suite/v2/review.rs:143 — test_review_multiple_threads

``
#[ignore = "TODO(owenlin0): flaky"]
``

1. codex-rs/tui/tests/suite/no_panic_on_startup.rs:9 — test_no_panic_on_startup

``
#[ignore = "TODO(mbolin): flaky"]
``

Additionally, two tests are ignored due to unimplemented features:

1. codex-rs/core/tests/suite/codex_delegate.rs:27 — test_codex_delegate_with_approval

``
#[ignore = "TODO once we have a delegate that can ask for approvals"]
``

1. codex-rs/core/tests/suite/codex_delegate.rs:119 — test_codex_delegate_with_rejection

``
#[ignore = "TODO once we have a delegate that can ask for approvals"]
``

Impact

• Flaky tests mask real race conditions or timing issues that users may encounter.
• Unimplemented feature tests indicate incomplete delegate approval/rejection functionality.

Suggested fix

• For the flaky tests: investigate the root cause of flakiness (likely timing/race conditions) and fix the underlying issue rather than ignoring the tests.
• For the delegate tests: either implement the approval flow or remove the dead test code.

Environment

• Files as listed above, main branch