Fix+test timedelta64(nat) ops
State: closed

Fixes issues mentioned as follow-ups to #23320

- [ ] closes #xxxx
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry


Labels:
name: Bug
name: Error Reporting
description: Incorrect or improved errors from pandas
name: Timedelta
description: Timedelta data type
name: Algos
description: Non-arithmetic algos: value_counts, factorize, sorting, isin, clip, shift, diff

Comments:
Hello @jbrockmendel! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/arrays/datetimelike.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/core/arrays/datetimelike.py) !

 - There are no PEP8 issues in the file [`pandas/core/arrays/period.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/core/arrays/period.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/base.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/core/indexes/base.py) !

 - There are no PEP8 issues in the file [`pandas/tests/arithmetic/test_datetime64.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/tests/arithmetic/test_datetime64.py) !

 - There are no PEP8 issues in the file [`pandas/tests/arithmetic/test_period.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/tests/arithmetic/test_period.py) !

 - There are no PEP8 issues in the file [`pandas/tests/arithmetic/test_timedelta64.py`](https://github.com/jbrockmendel/pandas/blob/f28f639f4be3dffe00f356cf0ecd5da59f1a376d/pandas/tests/arithmetic/test_timedelta64.py) !


# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23425?src=pr&el=h1) Report
> Merging [#23425](https://codecov.io/gh/pandas-dev/pandas/pull/23425?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/6bf6cd2fe991f4f57e045e1f28a9dff860b72b37?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/23425/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/23425?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #23425      +/-   ##
==========================================
+ Coverage   92.25%   92.25%   +<.01%     
==========================================
  Files         161      161              
  Lines       51186    51195       +9     
==========================================
+ Hits        47222    47231       +9     
  Misses       3964     3964
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.64% <100%> (ø)` | :arrow_up: |
| #single | `42.27% <23.07%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/23425?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/23425/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.46% <ø> (ø)` | :arrow_up: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/23425/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `96.16% <100%> (+0.06%)` | :arrow_up: |
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/23425/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `98.09% <100%> (ø)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23425?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/23425?src=pr&el=footer). Last update [6bf6cd2...6d3d38d](https://codecov.io/gh/pandas-dev/pandas/pull/23425?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

lgtm. can you rebase. ping on green.