[FEATURE] Configurable prompt cache TTL via env var

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

Use case: Working with 20-30 file codebases where pauses between
interactions cause cache misses. 1-hour TTL would reduce re-cache costs.

Request: Add env var like CLAUDE_CODE_CACHE_TTL accepting "5m" or "1h"
(matching the API's cache_control.ttl options).

The API already supports this - just needs exposure in Claude Code.

Proposed Solution

Just expose the feature that API currently has.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_