Mix EA into DTA/TDA; part of 24024
This is _nearly_ all of the remaining DTA/TDA changes in #24024.  The things that are not included:

- constructor changes
- fillna, since in local testing it alters DTA inplace, so not ready

`value_counts` from 24024 has small change to make sure the tz-aware case is correct regardless of how the constructor changes in 24024 get resolved.  A test is added specifically to check for this.

The changes implied by mixing ExtensionArray into DatetimeLikeArrayMixin are _not_ tested yet, won't be until the extension tests part of #24024 is merged.  I don't see any way around that except for doing 24024 all at once.
lgtm. ping on green. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=h1) Report
> Merging [#24502](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/9267e276bcbb86c67876b8eb94e865cdd55ac9b1?src=pr&el=desc) will **decrease** coverage by `49.26%`.
> The diff coverage is `30.43%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24502/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=tree)

```diff
@@             Coverage Diff             @@
##           master   #24502       +/-   ##
===========================================
- Coverage   92.31%   43.05%   -49.27%     
===========================================
  Files         166      166               
  Lines       52391    52400        +9     
===========================================
- Hits        48363    22559    -25804     
- Misses       4028    29841    +25813
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `?` | |
| #single | `43.05% <30.43%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `41.54% <100%> (-56.85%)` | :arrow_down: |
| [pandas/core/arrays/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3RpbWVkZWx0YXMucHk=) | `40% <16.66%> (-47.69%)` | :arrow_down: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `43.71% <31.25%> (-51.77%)` | :arrow_down: |
| [pandas/io/formats/latex.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvbGF0ZXgucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/core/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY2F0ZWdvcmljYWwucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/sas/sas\_constants.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfY29uc3RhbnRzLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/plotting.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvcGxvdHRpbmcucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvY29udmVydGVyLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `0% <0%> (-98.65%)` | :arrow_down: |
| [pandas/core/groupby/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ3JvdXBieS9jYXRlZ29yaWNhbC5weQ==) | `0% <0%> (-95.46%)` | :arrow_down: |
| ... and [127 more](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24502?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/24502?src=pr&el=footer). Last update [9267e27...5af756b](https://codecov.io/gh/pandas-dev/pandas/pull/24502?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/24502?src=pr&el=h1) Report
> Merging [#24502](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/9267e276bcbb86c67876b8eb94e865cdd55ac9b1?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `83.33%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24502/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24502      +/-   ##
==========================================
+ Coverage   92.31%   92.31%   +<.01%     
==========================================
  Files         166      166              
  Lines       52391    52400       +9     
==========================================
+ Hits        48363    48372       +9     
  Misses       4028     4028
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.73% <83.33%> (ø)` | :arrow_up: |
| #single | `43.04% <33.33%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `98.35% <100%> (-0.04%)` | :arrow_down: |
| [pandas/core/arrays/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3RpbWVkZWx0YXMucHk=) | `87.42% <66.66%> (-0.26%)` | :arrow_down: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `95.75% <87.5%> (+0.27%)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24502/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `97.91% <0%> (+0.17%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24502?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/24502?src=pr&el=footer). Last update [9267e27...5af756b](https://codecov.io/gh/pandas-dev/pandas/pull/24502?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 ping thanks