fix(gateway): stabilize Anthropic billing cch for cache

[mylukin]

Summary

• stabilize the rotating Claude Code billing cch on Anthropic native passthrough requests
• keep passthrough body semantics intact: preserve cc_version, cc_entrypoint, system/messages/tools/cache_control
• record anthropic_billing_cch_stabilized in passthrough mutations for auditability

Why

Production claude-fable-5 telemetry showed the official Claude Code billing header changes only cch every turn, which sits at system[0] and breaks Anthropic prompt-cache prefix matching. This is a cost-compatibility shim, not a broad passthrough rewrite.

Validation

• pnpm exec vitest run apps/gateway/src/routes/execute.test.ts
• pnpm typecheck
• pnpm exec biome check apps/gateway/src/routes/execute.ts apps/gateway/src/routes/execute.test.ts
• git diff --check

Note: full pnpm lint is currently blocked by an unrelated existing lint finding in packages/core/src/memory/forgetting/facts.test.ts:64.