DEPR: list of lists in Series.str.cat
The `.str.cat`-method is the only one in the `str`-accessor that takes another Series as an argument, and as such, is a bit of a special case (e.g. it had no index alignment until v0.23).

It makes sense to support lists of objects which get concatenated sequentially, and list of lists have been supported since at least v0.17, see https://pandas.pydata.org/pandas-docs/version/0.17.0/generated/pandas.Series.str.cat.html

When I wrote #20347, I tried very hard to keep signature backwards-compatible, and the example from the v0.17-22 docs working:
```
>>> Series(['a', 'b']).str.cat([['x', 'y'], ['1', '2']], sep=',')
0    a,x,1
1    b,y,2
dtype: object
```
However, this added lots of complexity, and I think that this should be simplified, especially in light of @TomAugspurger's comment in #21894
> As a reminder, the plan is to have no new deprecations in 0.25.x and 1.0.0. So this [v0.24] is the last round of deprecations before 1.0.

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`, which is currently a bit complicated. https://github.com/pandas-dev/pandas/blob/v0.23.3/pandas/core/strings.py#L2089

Finally, for completeness, the example from the v0.17-22 docs has been removed for v0.23, but there are two examples in https://pandas.pydata.org/pandas-docs/stable/text.html#concatenating-a-series-and-many-objects-into-a-series that would fall under the deprecation I'm suggesting.