POC: complete composition switchover
NOT FOR MERGING.  per @TomAugspurger 's request, we're done splitting off parts of #24024.  So this is just a proof of concept to get a handle on what parts that are left in 24024 are required for which goals.

This makes DTI._data a DTA and TDI._data a TDA, then goes through and changes stuff until the tests pass locally.  With the exception of a change to make TimedeltaIndex.union work, the changes are pretty much all taken from 24024 with minimal edits.
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=h1) Report
> Merging [#24556](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/aa7cb0138da6e20b356e8d9ae1f184e78a04189f?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `97.05%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24556/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24556      +/-   ##
==========================================
+ Coverage   92.33%   92.33%   +<.01%     
==========================================
  Files         166      166              
  Lines       52465    52483      +18     
==========================================
+ Hits        48442    48459      +17     
- Misses       4023     4024       +1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.75% <97.05%> (ø)` | :arrow_up: |
| #single | `43.03% <82.35%> (+0.03%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/internals/blocks.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2Jsb2Nrcy5weQ==) | `93.85% <100%> (+0.02%)` | :arrow_up: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `96.36% <100%> (+0.02%)` | :arrow_up: |
| [pandas/core/arrays/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3RpbWVkZWx0YXMucHk=) | `87.47% <100%> (+0.05%)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.27% <100%> (-0.03%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.92% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `97.94% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.47% <100%> (ø)` | :arrow_up: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `96.45% <50%> (-0.16%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24556?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/24556?src=pr&el=footer). Last update [aa7cb01...b245e31](https://codecov.io/gh/pandas-dev/pandas/pull/24556?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/24556?src=pr&el=h1) Report
> Merging [#24556](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/aa7cb0138da6e20b356e8d9ae1f184e78a04189f?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `97.05%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24556/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24556      +/-   ##
==========================================
+ Coverage   92.33%   92.33%   +<.01%     
==========================================
  Files         166      166              
  Lines       52465    52483      +18     
==========================================
+ Hits        48442    48459      +17     
- Misses       4023     4024       +1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.75% <97.05%> (ø)` | :arrow_up: |
| #single | `43.03% <82.35%> (+0.03%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/internals/blocks.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2Jsb2Nrcy5weQ==) | `93.85% <100%> (+0.02%)` | :arrow_up: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `96.36% <100%> (+0.02%)` | :arrow_up: |
| [pandas/core/arrays/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3RpbWVkZWx0YXMucHk=) | `87.47% <100%> (+0.05%)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.27% <100%> (-0.03%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.92% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `97.94% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.47% <100%> (ø)` | :arrow_up: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24556/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `96.45% <50%> (-0.16%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24556?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/24556?src=pr&el=footer). Last update [aa7cb01...b245e31](https://codecov.io/gh/pandas-dev/pandas/pull/24556?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
