DEPR/BUG: Do not ignore sort in concat for DatetimeIndex

[rhshadrach]

• closes DEPR: pd.concat special cases DatetimeIndex to sort even when sort=False #57335 (Replace xxxx with the GitHub issue number)
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

Continuation of #62752

There are three things I'd like to accomplish here:

1. Users passing sort=False get an unsorted result. This is a bug and should be fixed without deprecation.
2. Users not specifying sort do not get a change in behavior, but will get warned when enforcing the deprecation will change behavior.
3. Changing behavior of sort here with pandas' internal usage of concat does not break user code.

It seems (3) will be very hard to ascertain. There are many places where concat is used without specifying sort but (a) the index cannot be Datetime or (b) alignment has already been done so sort has no impact. I plan to take a deeper look into internal usage to see if this deprecation can impact other parts of the API, I've so far only found one in groupby.shift that I think we can call a bug.

To accomplish these, it seems to me that we need to do a somewhat expensive check to see if not sorting impacts the result as otherwise users will get many spurious warnings.

[rhshadrach]

@jbrockmendel - this is ready for a look. I still need to look more into the internal usages of concat as mentioned in the OP, but going to hold off until this looks to be the way forward.

[jbrockmendel]

I still need to look more into the internal usages of concat as mentioned in the OP, but going to hold off until this looks to be the way forward.

I'm fine with this. Though seeing the increased complexity, I'd also be OK with the previous PR's breaking change approach.

[rhshadrach]

I've reviewed all of pandas' internal usages of concat and fixed any behavior where we get inconsistent sorting due to the presence of a DatetimeIndex or not as bugs. See the whatsnew. Ran into #62954 here, once that is merged this will be good for review.

[jbrockmendel]

LGTM pending #62954

[jbrockmendel]

thanks @rhshadrach