fix Series.apply(..., by_row)

[topper-123]

Fixes #53400 (comment) by making the by_row param take no_default as its default parameter.

[rhshadrach]

This moves in the right direction, but I think we still run into issues with the deprecation.

df = pd.DataFrame({'a': [1, 1, 2], 'b': [3, 4, 5]})

# On 2.0.x
print(df.apply([lambda x: 1]))
#          a        b
#   <lambda> <lambda>
# 0        1        1
# 1        1        1
# 2        1        1

# On main
print(df.apply([lambda x: 1]))
#           a  b
# <lambda>  1  1

Here, pandas is internally calling agg, which then splits up the DataFrame.agg into Series.agg on each column, and then this calls Series.apply. So we end up in Series.apply but with no way for the user to specify by_row=False.

One way around this would be to stop breaking up the DataFrame.agg into Series.agg calls and instead breakup the list func into individual DataFrame.agg calls, but then we run into #45658. If we try to do this without changing the behavior, we end up losing dtype information because of the transpose.

The only other way I see forward is to add a by_row argument to DataFrame.apply that is only used for list-likes (and maybe dict-likes?). This seems not straightforward from a user perspective. Maybe I'm overlooking another alternative?

[topper-123]

I've made a new PR for this, see #53601, so I'm closing this.