feat(relay): hosted-tool conversion fidelity, reasoning normalization, and billing usage integrity (#7137)
* feat(relaykit): preserve hosted tools across conversions
- add protocol-neutral hosted-tool DTOs, conversion metadata, and loss policies
- bridge citations, grounding metadata, and hosted-tool stream lifecycles
- document the public conversion behavior and channel policy controls
* refactor(relaykit): normalize reasoning and thinking intent
- centralize provider-neutral reasoning intent, effort, and budget mappings
- parse model suffixes at the host entry boundary while preserving provider-owned tails
- keep adaptive Claude thinking and explicit zero-token compatibility consistent
* fix(billing): preserve authoritative usage across relay hops
- carry native BillingUsage sidecars through direct and streamed protocol bridges
- merge partial and terminal usage monotonically with safe fallback settlement
- retain cache metadata, penultimate usage, and per-call Gemini tool surcharges
* feat(relay): bridge Responses with Claude and Gemini protocols
- add direct request, response, and stream converters across supported relay formats
- expose Claude count_tokens and Chat-to-Responses compatibility endpoints
- carry conversion diagnostics through the host while retaining the curated public goldens
* fix(relay): wire relaykit conversions into host channels
- connect handlers, adaptors, and channel settings to the standalone conversion layer
- keep model mapping, pricing identity, retries, and provider-specific suffix behavior aligned
- ignore local audit artifacts and retain focused public regression coverage
