[C++] Use `JsonWriter` consistently in `LogicalType::ToJSON()`

[Reranko05]

Describe the enhancement requested

LogicalType::ToJSON() currently mixes manual JSON string construction with ::arrow::json::JsonWriter.

Refactor it to use JsonWriter for building the entire JSON object to improve consistency and maintainability.

Parent Issue: #35460

Component(s)

C++

[NathanChung4]

take

[pitrou]

Issue resolved by pull request 50877
#50877