[C++][Integration] Replace RapidJSON with simdjson #50936

Describe the enhancement requested

Describe the enhancement requested

The C++ integration JSON implementation under cpp/src/arrow/integration uses RapidJSON for JSON parsing and serialization.

Replace the RapidJSON usage with simdjson and Arrow's existing JsonWriter, removing the remaining RapidJSON dependency from the integration implementation while preserving the existing JSON integration behavior and test coverage.

Additional context

Parent Issue: GH-35460.

Component(s)

C++