TST: Add test to verify DataFrame's constructor doesn't convert Nones to strings on string columns
- [x] closes #32218
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them

### whatsnew
Adds a very simple test to verify that `None`s are not casted to strings as `"None"` inside the DataFrame's constructor for string columns.

Questions:
* Should the test be more general?
* What is the proper location for the test?

This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. @cgarciae can you merge master to resolve conflicts and can take a look closing as stale