DEPR: Deprecate tshift and integrate it to shift
- [x] closes #11631
- xref #34452
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

thanks. would not be averse to actually re-writing tshift in terms of shift; I *think* this would be straightforward. Also could merge this and then followon to do that. > would not be averse to actually re-writing tshift in terms of shift; I think this would be straightforward

Agree it's rather straightforward, but just to clarify a few things: 
1. we are still going to deprecate `tshift` after the re-write right? In other words, you don't mean to re-write and **keep** `tshift` right?
1. do you think it's better to move the current `_tshift` inside `shift`? i.e. we won't have a separate method `_tshift`, but unpack what's in it and put inside `shift` > > would not be averse to actually re-writing tshift in terms of shift; I think this would be straightforward
> 
> Agree it's rather straightforward, but just to clarify a few things:
> 
> 1. we are still going to deprecate `tshift` after the re-write right? In other words, you don't mean to re-write and **keep** `tshift` right?

correct, still deprecate

> 2. do you think it's better to move the current `_tshift` inside `shift`? i.e. we won't have a separate method `_tshift`, but unpack what's in it and put inside `shift`

yes if possible (ideally simplified as much as possible).

 Have unpacked previous `_tshift` and moved into `shift`, also simplified the code a little bit. The deprecating `tshift` now calls `shift`. @jreback can you review? @fujiaxiang can you rebase and some small comments, ping on green. @jreback have split up the tests into PI and DTI and also separated the failure tests
I tried to parametrize the test cases into PI and DTI but I realize they only have a very small proportion of code in common, so I decided to separate them into different tests > @jreback have split up the tests into PI and DTI and also separated the failure tests
> I tried to parametrize the test cases into PI and DTI but I realize they only have a very small proportion of code in common, so I decided to separate them into different tests

kk sounds good. ping on green (note that there maybe be a failure on master that is unrelated) thanks @fujiaxiang very nice