DEPR: list-likes of list-likes in str.cat
- [x] closes #21950
- [x] tests modified / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

As mentioned in #21950, my suggestion is to modify the allowed combinations (as of v0.23) as follows:
```
Type of "others"                        |  action  |  comment
---------------------------------------------------------------------
list-like of strings                    |   keep   |  as before; mimics behavior elsewhere,
                                                      cf.: pd.Series(range(3)) + [2,4,6]
Series                                  |   keep   |
np.ndarray (1-dim)                      |   keep   |
DataFrame                               |   keep   |  sequential concatenation
np.ndarray (2-dim)                      |   keep   |  sequential concatenation
list-like of
    Series/Index/np.ndarray (1-dim)     |   keep   |  sequential concatenation
list-like containing list-likes (1-dim)
    other than Series/Index/np.ndarray  |   DEPR   |  sequential concatenation
```

In other words, if the user wants sequential concatenation, there are many possibilities available, and list-of-lists does not have to be one of them, IMO. This would substantially simplify (post-deprecation) the code for `str.cat._get_series_list`: 


```
def _get_series_list(self, others):
    """
    Auxiliary function for :meth:`str.cat`. Turn potentially mixed input
    into a list of Series (elements without an index must match the length
    of the calling Series/Index).

    Parameters
    ----------
    others : Series, DataFrame, np.ndarray, list-like or list-like of
        objects that are either Series, Index or np.ndarray (1-dim)

    Returns
    -------
    list : others transformed into list of Series
    """
    from pandas import Index, Series, DataFrame

    # self._orig is either Series or Index
    idx = self._orig if isinstance(self._orig, Index) else self._orig.index

    # Generally speaking, all objects without an index inherit the index
    # `idx` of the calling Series/Index - i.e. must have matching length.
    # Objects with an index (i.e. Series/Index/DataFrame) keep their own.
    if isinstance(others, Series):
        return [others]
    elif isinstance(others, Index):
        return [Series(others.values, index=others)]
    elif isinstance(others, DataFrame):
        return [others[x] for x in others]
    elif isinstance(others, np.ndarray) and others.ndim == 2:
        others = DataFrame(others, index=idx)
        return [others[x] for x in others]
    elif is_list_like(others):
        others = list(others)  # ensure iterators do not get read twice etc

        # in case of list-like `others`, all elements must be
        # either Series/Index/np.ndarray (1-dim)...
        if all(isinstance(x, (Series, Index))
               or (isinstance(x, np.ndarray) and x.ndim == 1) for x in others):
            los = []
            while others:  # iterate through list and append each element
                los = los + self._get_series_list(others.pop(0))
            return los
        # ... or just strings
        elif all(not is_list_like(x) for x in others):
            return [Series(others, index=idx)]
    raise TypeError('others must be Series, Index, DataFrame, np.ndarrary or '
                    'list-like (either containing only strings or containing '
                    'only objects of type Series/Index/np.ndarray[1-dim])')
```
