DEPR: Deprecate literal json string input to read_json
- [X] closes #52271
- [x] [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
- [x] 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.

**Code Checks / Docstring validation, typing, and other manual pre-commit hooks (pull_request)** test failing seems to be unrelated to changes in my PR.

**Doc Build and Upload** seems to be failing because the CI test itself passes literal JSON strings to `read_json`. This doesn't seem like something that I can fix myself?

 @mroeschke Would you be able to take a look at this PR and let me know if anything needs updating? @mroeschke This PR should be ready for review! @mroeschke This PR should be ready for review! @mroeschke PR is ready for review. 

I believe I have addressed your concerns. From what I can tell, the test failures in Numpy Dev are not related to my PR Could you merge in the main branch too? @mroeschke Should be good to go now.  Looks like some of the code checks are still failing in the CI @mroeschke Code Checks / Docstring validation passing now. Docbuild and upload test failure doesn't appear to be associated with PR  You may want to check usage of `read_json` in the the `doc/source` folder for the deprecated behavor. PRs should still pass the doc build @mroeschke Pinging on green! @mroeschke Should be good to go now! Thanks @rmhowe425 