BUG: Fix StringArray use_inf_as_na bug
- [x] closes #33655
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

you also have #33629  for this same issue? > you also have #33629 for this same issue?

We were thinking we may want to treat them separately since they're slightly different issues: https://github.com/pandas-dev/pandas/pull/33629#discussion_r410871916. Should both bugs be in the same PR? Can you also add a test somewhere for an object dtype Series that has pd.NA in it? (that won't be covered by the string dtype tests)

This shouldn't be "draft" anymore? > This shouldn't be "draft" anymore?

I was hoping to finish up the PR linked above first because it overlaps somewhat with this one Does this address #33209? > Does this address #33209?

Yes I think it should > Can you also add a base extension test for this? (there should already be `isna()` tests, so you can add a similar one there but which is using `use_inf_as_na`

Added some base extension use_inf_as_na tests, however I'm getting failures from test_sparse.py (dtype-related, I believe), test_json.py and test_decimal.py (the latter two I think because of improper handling of null values; e.g., {} and Decimal("NaN") under the use_inf_as_na context). Should I xfail for these for now and try to address in a follow-up? @dsaxton can you merge master once more?

And what is left for this PR? I think only the comment of @jbrockmendel to not do the expensive `libmissing.isnaobj_old(values.to_numpy())` check for certain dtypes where this will never be needed (like Periods) ? 
 > And what is left for this PR?

@jorisvandenbossche There was also this issue that I still need to figure out (I think it could potentially be fixed with the short circuiting mentioned above): https://github.com/pandas-dev/pandas/pull/33656#issuecomment-621947813 @jreback ping thanks @dsaxton 