DOC: document public/private subpackages in api.rst
WIP (have to run now)
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=h1) Report
> Merging [#16087](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/fcd2f70d369ad0abdefd9026b71e416dfc3e82d9?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/16087/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #16087      +/-   ##
==========================================
+ Coverage   90.84%   90.85%   +<.01%     
==========================================
  Files         159      159              
  Lines       50774    50790      +16     
==========================================
+ Hits        46127    46143      +16     
  Misses       4647     4647
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.63% <ø> (ø)` | :arrow_up: |
| #single | `40.36% <ø> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/api.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL2lvL2FwaS5weQ==) | `71.42% <0%> (-28.58%)` | :arrow_down: |
| [pandas/util/hashing.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvaGFzaGluZy5weQ==) | | |
| [pandas/formats/style.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL2Zvcm1hdHMvc3R5bGUucHk=) | | |
| [pandas/tools/hashing.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL3Rvb2xzL2hhc2hpbmcucHk=) | `99.02% <0%> (ø)` | |
| [pandas/util/importing.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvaW1wb3J0aW5nLnB5) | `0% <0%> (ø)` | |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `79.62% <0%> (+0.24%)` | :arrow_up: |
| [pandas/plotting/\_converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb252ZXJ0ZXIucHk=) | `65.35% <0%> (+1.81%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/16087?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/16087?src=pr&el=footer). Last update [fcd2f70...bee8769](https://codecov.io/gh/pandas-dev/pandas/pull/16087?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
