Backport PR #17747 on branch v7.0.x (Ensure doctests do not have side effects) - #17751

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@mhvk any idea why this doctest fails in backport but not on main? 🤔

_________________________ [doctest] mixin_columns.rst __________________________
...
364 By default, the outcome of setting a column using this class is not helpful::
365 
366     >>> t = Table([np.arange(4)], names=["index"])
367     >>> t['data'] = ExampleDataClass()
UNEXPECTED EXCEPTION: NameError("name 'ArrayWrapper' is not defined")
Traceback (most recent call last):
  File "python3.11/doctest.py", line 1355, in __run
    exec(compile(example.source, filename, "single",
  File "<doctest mixin_columns.rst[33]>", line 1, in <module>
  File "astropy/table/table.py", line 2110, in __setitem__
    self.add_column(value, name=item, copy=True)
  File "astropy/table/table.py", line 2404, in add_column
    col = self._convert_data_to_col(
          ^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "astropy/table/table.py", line 1323, in _convert_data_to_col
    data = handler(data)
           ^^^^^^^^^^^^^
  File "<doctest mixin_columns.rst[36]>", line 2, in handle_example_data_class
NameError: name 'ArrayWrapper' is not defined
docs/table/mixin_columns.rst:367: UnexpectedException

I think we'd need to backport a previous fix to the registry or so, since the .rst file hasn't changed. But it seemed easier to just fix it here... I wonder if I should "forward-port" this regardless of the fact that it doesn't fail. Probably not?

Re: forward-port -- Hmm I dunno if the universe is going to explode or not if we forward port a backport, but can try after merge?

Let's see if anything explodes...

@meeseeksdev backport to main