ENH: Support TZ Aware IntervalIndex
State: closed

- [X] closes #18537
- [X] closes #18538
- [X] tests added / passed
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [X] whatsnew entry

Updates to `Interval`:
- Disallowed `Interval` objects with mixed time zones
- Minor docstring updates

Updates to `IntervalIndex`:
- Disallowed `IntervalIndex` with mixed time zones
- Fixed `IntervalIndex.mid` for tz aware
- Fixed `_get_next_label` and `_get_previous_label` for tz aware
   - cascades to other methods
- Cleaned up error message for mixed `left`/`right` types


Labels:
name: Timezones
description: Timezone data dtype
name: Interval
description: Interval data type

Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=h1) Report
> Merging [#18558](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/32f562dbe459ee9e437da3a67631949d34531411?src=pr&el=desc) will **decrease** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18558/graphs/tree.svg?token=eZ4WkYLtcO&width=650&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18558      +/-   ##
==========================================
- Coverage   91.35%   91.34%   -0.01%     
==========================================
  Files         164      164              
  Lines       49802    49813      +11     
==========================================
+ Hits        45496    45502       +6     
- Misses       4306     4311       +5
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.14% <100%> (+0.01%)` | :arrow_up: |
| #single | `40.8% <25%> (-0.07%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `94.02% <100%> (+0.8%)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558?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/18558?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/18558?src=pr&el=footer). Last update [32f562d...2311143](https://codecov.io/gh/pandas-dev/pandas/pull/18558?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/18558?src=pr&el=h1) Report
> Merging [#18558](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/695e89345a46c0cab06c479c83007f5adbb70ad5?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/18558/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18558      +/-   ##
==========================================
- Coverage   91.59%   91.58%   -0.02%     
==========================================
  Files         153      153              
  Lines       51212    51217       +5     
==========================================
- Hits        46908    46906       -2     
- Misses       4304     4311       +7
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.44% <100%> (ø)` | :arrow_up: |
| #single | `40.67% <28.57%> (-0.11%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `93.8% <100%> (+0.74%)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `81.82% <0%> (-0.2%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18558/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/18558?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/18558?src=pr&el=footer). Last update [695e893...79e255c](https://codecov.io/gh/pandas-dev/pandas/pull/18558?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

Fixed the `mid` computation now that #18653 is merged.  I believe that was the last item that was currently outstanding here.
thanks @jschendel