[BUG] askUserQuestionTimeout set to "60s" never auto-continues a question (v2.1.270, macOS)

**Environment**

- Claude Code 2.1.270
- macOS 26.6.2
- VS Code integrated terminal 1.136.1, no tmux
- Launched as `claude --dangerously-skip-permissions`, with no `--remote-control` flag
- The session is long and uses many `AskUserQuestion` calls, some with previews and several questions in one call

**Setting**

`~/.claude/settings.json` has this at the top level, and the file parses as valid JSON:

```json
"askUserQuestionTimeout": "60s"
```

Nothing overrides it. None of these files exist:

- `/Library/Application Support/ClaudeCode/managed-settings.json`
- `/etc/claude-code/managed-settings.json`
- `/.claude/settings.local.json`
- `~/.claude/settings.local.json`

**Expected**

From the tools reference, under "Question auto-continue timeout": after a question sits for 60 seconds with no input, a countdown shows for the last 20 seconds, then the dialog closes, submits any options already selected, and tells Claude the user may be away.

**Actual**

The user reports that questions never time out. They stay open indefinitely until answered, with no countdown.

**Unverified**

- Whether the user touched the terminal during those waits. The docs say any keypress, or focusing a terminal that reports focus, restarts the timer. The user reports leaving questions unanswered well past 60 seconds.
- Whether the session was being followed through Remote Control from another device at the time. The Remote Control page says questions stay open until answered, and does not say whether `askUserQuestionTimeout` still applies there. If it does not, the settings reference should say so.

**Related**

- #73435, which made the timeout configurable
- #73986, docs on the timeout becoming opt-in
- #78125, a question continuing without an answer, which is the opposite symptom
- #77602, questions auto-resolving in `--remote-control` sessions with the setting unset

Start with the top-level askUserQuestionTimeout in ~/.claude/settings.json and reproduce the AskUserQuestion flow after 60 seconds without input. Compare a normal session with a --remote-control session, checking whether the countdown, dialog closure, option submission, and away notice occur; done means the behavior is corrected or the settings and Remote Control documentation clearly state the supported behavior.

Written by the indexing model from the issue text.