Feature request: surface prompt cache expiry status in CLI status bar

Summary

Add cache freshness visibility to the Claude Code CLI so users can make informed decisions about keep-alive messages vs. letting the cache lapse.

Proposed UX (three tiers, pick any)

1. Live countdown: "cache warm (4:23 until expiry)"
2. Simple state indicator: green dot "cache warm" / yellow "expiring soon" / red "cache cold"
3. Timestamp: last cache-touching API call shown in status line

Why this matters

For users running expensive models (Opus) or long sessions with subagents, knowing when to send a keep-alive message vs. letting the cache lapse is currently a guessing game. The 5-minute TTL is documented but not surfaced anywhere in the interface.

Concrete workflow impact: when orchestrating multi-agent pipelines with background tasks, I routinely lose cache state between agent calls because I have no signal that expiry is imminent. A simple indicator would let me time a lightweight keep-alive message before the window closes — meaningful cost-control for sessions that run $10–50+ in cached tokens.

Environment

Claude Code CLI, all platforms.