[backport 2.3.x] TST (string dtype): un-xfail string tests specific to object dtype (#59433)
(cherry picked from commit dbeeb1f05bca199b3c1aed979e6ae72074a82243)

Backport of https://github.com/pandas-dev/pandas/pull/59433
Will wait with further updating this depending on https://github.com/pandas-dev/pandas/pull/60183 This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this.