fix(tui): preserve queued follow-ups after capacity errors

[relh]

What

Keep Tab-queued follow-up inputs pending when an active TUI turn terminalizes with a structured ServerOverloaded error. Successful turn completion continues to advance the queue normally.

Candidate fix for openai#33853, held in the fork pending the maintainer invitation required by upstream's external-contribution policy.

Why

The overload handler currently finalizes the failed turn and immediately calls maybe_send_next_queued_input(). A dependent follow-up can therefore begin against partial side effects and incomplete conversation state from the failed prerequisite turn.

This is intentionally separate from same-turn capacity retry work such as openai#31058: even after a retry budget is exhausted, dependent queued work should not cascade automatically.

How

• Stop draining queued input from the terminal server-overload handler.
• Preserve the existing warning and turn-finalization behavior.
• Extend app-server lifecycle coverage through both the non-retry overload error and the subsequent failed turn/completed notification.
• Assert that no new Op::UserTurn is emitted and that the queued text remains available for review.

Validation

• just test -p codex-tui live_app_server_server_overloaded_error_preserves_queued_follow_up
• just test -p codex-tui (3,094 passed; 4 pre-existing skipped)
• just fix -p codex-tui
• just fmt