Pi: add session-affinity headers and sanitized prompt-cache diagnostics

[dgokeeffe]

Problem

Pi sessions can be routed across multiple AI Gateway destinations when traffic splitting is configured. Prompt caches are destination-local, so a conversation needs session-affinity headers to avoid avoidable cache misses.

Cache-retention investigations also need reproducible, sanitized tooling. Current observations do not prove that GPT subagents have short retention: GPT-5.6 Sol rejects explicit in_memory, and observed expiry may be caused by UAG forwarding, backend eviction, or prefix matching.

Expected behavior

• Enable Pi's production-safe session-affinity compatibility behavior.
• Add opt-in diagnostic scripts that send stable prompt-cache prefixes and report cache usage without printing bearer tokens.
• Cover 24h, provider-default, and explicit in_memory request construction.
• Validate phase-separated saved state and fail cleanly on malformed state.
• Preserve the measured 45/50/60-minute evidence without claiming a backend retention guarantee.
• Do not force PI_CACHE_RETENTION or install a child/subagent short-cache policy.