[C++][Dataset] Replace RapidJSON with JsonWriter in JSON Dataset #50913

Describe the enhancement requested

The Dataset JSON test currently uses RapidJSON for generating JSON test data in cpp/src/arrow/dataset/file_json_test.cc.

Replace the RapidJSON-based writer with Arrow's existing json::JsonWriter, removing the direct RapidJSON dependency while preserving the existing test behavior and JSON output.

Additional context

Parent Issue: #35460

Component(s)

C++