gh-119182: Use public PyUnicodeWriter in _json.c

[vstinner]

Replace the private _PyUnicodeWriter API with the public PyUnicodeWriter API.

• Issue: [C API] Add an efficient public PyUnicodeWriter API #119182

[cmaloney]

Have a plan for _PyUnicodeWriter_IsEmpty?

[vstinner]

Have a plan for _PyUnicodeWriter_IsEmpty?

My plan is to leave it in _json.c for now :-) I would prefer to not make it public, unless more people ask for such feature.

Also, the function can be removed and replaced with an empty variable. I just tried to minimize changes in my PR.