Use the JSON-serialized SearchRequestData for request-passing to the search isolate.

[isoos]

• Follow-up to Search handler and client with HTTP POST-based request serialization. #8892 and Search refactor: moving all internal serialization method to SearchRequestData #8895, updating the internal message-passing to JSON.
• There is no backward-compatibility issue here, since this is an internal detail of the isolate and won't be accessed in another way.