## Why
Preparing Responses API requests rebuilt tool definitions as a generic JSON
tree, and incremental WebSocket requests cloned their full item prefix for
comparison.
## What changed
- Serialize tool definitions into shared raw JSON that can be embedded directly
in HTTP and WebSocket requests.
- Compare incremental request prefixes in place while still ignoring internal
message metadata.
## Testing
- Verify raw tool JSON matches the existing value encoding.
- Preserve the serialized WebSocket request payload.
GitOrigin-RevId: 66e2921792c332e8904954dafa597f6d39abcf29