BUG: Fix tz-aware DatetimeIndex +/- TimedeltaIndex/timedelta64 array
State: closed

- [X] closes #17558
- [X] tests added / passed
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [X] whatsnew entry

Added the whatsnew entry under 0.22.0, but could possibly go under 0.21.1.  This PR is a prereq for #18558.

Labels:
name: Bug
name: Datetime
description: Datetime data dtype
name: Timedelta
description: Timedelta data type
name: Timezones
description: Timezone data dtype

Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=h1) Report
> Merging [#18653](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/13f6267207dd1f140b12d7718277508eff5c1efb?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18653/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18653      +/-   ##
==========================================
- Coverage   91.59%   91.57%   -0.02%     
==========================================
  Files         153      153              
  Lines       51221    51223       +2     
==========================================
- Hits        46917    46909       -8     
- Misses       4304     4314      +10
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.44% <100%> (-0.01%)` | :arrow_down: |
| #single | `40.67% <0%> (-0.11%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.6% <100%> (-0.09%)` | :arrow_down: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `97.13% <100%> (ø)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.81% <0%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18653?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/18653?src=pr&el=footer). Last update [13f6267...cc6b19b](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=h1) Report
> Merging [#18653](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/fdba133336c2ec8f1269eb15e73d48797840c48b?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/18653/graphs/tree.svg?token=eZ4WkYLtcO&src=pr&width=650&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18653      +/-   ##
==========================================
+ Coverage   91.57%   91.57%   +<.01%     
==========================================
  Files         153      153              
  Lines       51210    51212       +2     
==========================================
+ Hits        46894    46899       +5     
+ Misses       4316     4313       -3
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.43% <100%> (+0.02%)` | :arrow_up: |
| #single | `40.67% <0%> (-0.11%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `97.13% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.68% <100%> (ø)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.81% <0%> (-0.1%)` | :arrow_down: |
| [pandas/plotting/\_converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/18653/diff?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb252ZXJ0ZXIucHk=) | `65.25% <0%> (+1.81%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18653?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/18653?src=pr&el=footer). Last update [fdba133...2a665c0](https://codecov.io/gh/pandas-dev/pandas/pull/18653?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

thanks @jschendel 

very nice; keep em coming!