[FEATURE] Make AskUserQuestion tool timeout configurable

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

In day-to-day usage, there are many situations where 5 minutes is not enough:

• Context switching: I often kick off a long-running task in Claude Code, switch to another window/meeting/IDE, and come back later. If Claude asks a clarifying question while I'm away, the question silently times out and the task is aborted or proceeds with a default — wasting the work already done.
• Deep-thought questions: Some questions (architectural choices, reviewing a multi-option plan) genuinely take more than 5 minutes to think through, especially when I need to read code, check docs, or consult a teammate before answering.
• Long-running agent runs: When running multi-step agent workflows (sub-agents, plans, parallel tasks), a single timed-out question can break the entire chain.
• Pair / async workflows: When working with a colleague or in async mode, a 5-minute window is often too short.

The current behavior forces me to either (a) babysit the terminal, or (b) re-run the entire task from scratch after a timeout, which is wasteful.

Proposed Solution

Expose the timeout as a user-configurable setting. Any of the following would work; I'd be happy with any one of them, ideally a combination:

1. settings.json field, e.g.:

```json
{
"askUserQuestionTimeoutMs": 1800000 // 30 minutes
}
2 Environment variable, e.g. CLAUDE_ASK_USER_TIMEOUT_MS=1800000.

1. CLI flag, e.g. claude --ask-timeout 30m.
2. Special value for "no timeout", e.g. 0 or -1 meaning "wait indefinitely until the user answers".

A sensible default (e.g. keep 5 minutes) is fine; the key request is letting users override it.

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_