New per-turn timing signal for requests

What

Claude Code can now include the current timestamp with each turn it sends to the model, as a new field alongside the existing per-turn effort mechanism. This only happens when a new beta flag is enabled and the CLAUDE_CODE_PER_TURN_TIMING environment variable is set, together with the existing eligibility checks used for per-turn effort.

• A new per-request field injects the current time into each turn's request when the beta flag and environment variable enable it.
• The internal list of flags used to build prompts and decide cache validity now includes per_turn_timing next to the existing per_turn_effort.

Why

This is a gated, opt-in signal, so it has no effect unless CLAUDE_CODE_PER_TURN_TIMING is set. Once enabled, it lets the model be aware of timing information on a per-turn basis, similar to how per-turn effort already works.