WIP: Dispatch Series comparison methods to Index implementations
State: closed

Same thing we've been doing for arithmetic operations, now moving on to comparison methods.  Based on some trial-and-error, it seems like there are some inconsistencies to be worked out for the categorical dtype case.  This PR:

- Dispatches timedelta and datetime `Series` comparisons to their respective `Index` subclass implementations
   - Patches `DatetimeIndex._assert_tz_awareness_compat`, which has already been broken out into #19276.
   - Kludges `datetime.date` and `None` case that `Series` treats differently from `DatetimeIndex`; decisions should be made about those so these kludges can be removed.
- Removes a `# temp workaround until fixing GH 13637` for comparison with `PeriodIndex` that appears to no longer be needed.
- Fixes names of the results for comparisons between `Series` and `Index` classes. (probably needs tests)
- Notes some small inconsistencies in how `_constructor` is called, also discussed in #19271.

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Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/19288?src=pr&el=h1) Report
> Merging [#19288](https://codecov.io/gh/pandas-dev/pandas/pull/19288?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/d7a2e94914b7707e1c37a4524a9a7c3fef649d01?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `94.73%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/19288/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/19288?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #19288      +/-   ##
==========================================
+ Coverage   91.56%   91.56%   +<.01%     
==========================================
  Files         148      148              
  Lines       48888    48881       -7     
==========================================
- Hits        44765    44760       -5     
+ Misses       4123     4121       -2
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.94% <94.73%> (ø)` | :arrow_up: |
| #single | `41.69% <52.63%> (+0.01%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/19288?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.33% <100%> (+0.09%)` | :arrow_up: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `91.73% <94.28%> (-0.44%)` | :arrow_down: |
| [pandas/io/parquet.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3BhcnF1ZXQucHk=) | `69.9% <0%> (-1.66%)` | :arrow_down: |
| [pandas/io/s3.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3MzLnB5) | `85% <0%> (-1.37%)` | :arrow_down: |
| [pandas/io/parsers.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3BhcnNlcnMucHk=) | `95.48% <0%> (-0.02%)` | :arrow_down: |
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `95.9% <0%> (-0.01%)` | :arrow_down: |
| [pandas/io/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2NvbW1vbi5weQ==) | `69.06% <0%> (ø)` | :arrow_up: |
| [pandas/core/internals.py](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzLnB5) | `94.5% <0%> (ø)` | :arrow_up: |
| ... and [1 more](https://codecov.io/gh/pandas-dev/pandas/pull/19288/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/19288?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/19288?src=pr&el=footer). Last update [d7a2e94...2a77d63](https://codecov.io/gh/pandas-dev/pandas/pull/19288?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

I can’t replicate appveyor error locally. Something windows specific?
Closing until #19301