[FEATURE] Idle-time tasks: run deferrable background tasks when spare capacity is available, without consuming usage limits

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

A lot of my Claude Code work is deferrable: coverage sweeps, flaky-test investigations, dependency upgrade research, bulk refactors, doc cleanups. None of it needs to start now, but the only way to run it is in the foreground — consuming usage limits at peak times. So I either skip that work or pay peak prices for work whose timing doesn't matter. There is no way to hand Claude Code a task to execute "later, when compute is cheap".

Proposed Solution

Idle-time tasks (similar to Z.ai ZCode's feature of the same name):

• I register a self-contained task: title + instructions + expected result and constraints.
• The task enters a queue and runs unattended in the same session/workspace (full context retained) when Anthropic has spare capacity — no guaranteed start time.
• Model calls during such runs go through an off-peak channel and don't count against plan usage limits (or a clearly communicated discounted multiplier).
• Actions needing confirmation pause the task until I respond, since runs are unattended.

Additional context

Prior art: ZCode (Z.ai) ships idle-time tasks — a queue with free execution when spare compute is available. Docs: https://zcode.z.ai/cn/docs/idle-time-tasks; OSS client implementation: https://github.com/zai-org/ZCode (packages/services/src/session/offPeakMockGateway.ts shows the take → queued → ready → active → settle protocol). Feature request filed on their tracker: zai-org/feedback#793.