ENH: Deprecate literal json string input to read_json
- [X] closes #52271 
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [X] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [X] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

@mroeschke This looks like its going to be a pretty bulky PR after all of the unit tests are updated. 

Was hoping that someone could make sure that I'm on the right track before I finish updating the remainder of the unit tests? Do we want to achieve the consistency as mentioned in https://github.com/pandas-dev/pandas/issues/52271#issuecomment-1490202911 in this PR? If not, maybe open a follow-up issue with the xref.