DEPR: passing timedelta-like to DatetimeIndex constructor, xref #23675
Implements the agreed-upon portions of #23675 so we can keep moving the ball down the field.

- [ ] closes #xxxx
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Hello @jbrockmendel! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/arrays/datetimes.py`](https://github.com/jbrockmendel/pandas/blob/2792dcb801a4fb126ea7ea9c655b702bac14cc22/pandas/core/arrays/datetimes.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/datetimes.py`](https://github.com/jbrockmendel/pandas/blob/2792dcb801a4fb126ea7ea9c655b702bac14cc22/pandas/core/indexes/datetimes.py) !

 - There are no PEP8 issues in the file [`pandas/core/tools/datetimes.py`](https://github.com/jbrockmendel/pandas/blob/2792dcb801a4fb126ea7ea9c655b702bac14cc22/pandas/core/tools/datetimes.py) !

 - There are no PEP8 issues in the file [`pandas/tests/indexes/datetimes/test_construction.py`](https://github.com/jbrockmendel/pandas/blob/2792dcb801a4fb126ea7ea9c655b702bac14cc22/pandas/tests/indexes/datetimes/test_construction.py) !

 lgtm. add to #6581 ping on green. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=h1) Report
> Merging [#23937](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/ede0dae3b74a5b9cba11ad6d86fcbc92329f631c?src=pr&el=desc) will **decrease** coverage by `<.01%`.
> The diff coverage is `97.36%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/23937/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #23937      +/-   ##
==========================================
- Coverage   92.29%   92.29%   -0.01%     
==========================================
  Files         161      161              
  Lines       51501    51523      +22     
==========================================
+ Hits        47534    47554      +20     
- Misses       3967     3969       +2
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.69% <97.36%> (ø)` | :arrow_up: |
| #single | `42.43% <76.31%> (+0.01%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/23937/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.18% <100%> (-0.02%)` | :arrow_down: |
| [pandas/core/tools/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/23937/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvdG9vbHMvZGF0ZXRpbWVzLnB5) | `85.44% <100%> (+0.18%)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/23937/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `98.37% <95.23%> (-0.14%)` | :arrow_down: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/23937/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `94.14% <0%> (-0.14%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=footer). Last update [ede0dae...2792dcb](https://codecov.io/gh/pandas-dev/pandas/pull/23937?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 azure failure is Hypothesis.  de-facto green ping thanks. do we need to simply raise the timeout on hypthossis? > do we need to simply raise the timeout on hypthossis?

I think I saw a PR for that recently.  Didn't look at it too closely.  If I'm going to spend time on one minor annoyance today, it'll be the dateutil DeprecationWarning.