opt out of bottleneck for nanmean
- [x] closes #42878
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Hello @sebasv! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:





There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2022-07-17 13:11:07 UTC I added 2 unit tests to validate that numerical precision is bounded by log(n). If anyone has suggestions how to improve these tests let me know @mroeschke I will verify this. Addition is pure for integers so depending on the bottleneck implementation it should be almost exact Glad to see this update.  Should it be targeting pandas 1.5.0 or 1.4.4 release? > Glad to see this update. Should it be targeting pandas 1.5.0 or 1.4.4 release?

1.5. Point releases are reserved for regression in behavior from recent releases. Integer mean should also be opted out of. In the case of integer arrays it seems that bottleneck accumulates the sum in a float64 type, wich means that the problem persists there as well. I'm adding int types to the unit test as well

Example 
```python
>>> a = np.full((1_000_000_000, 1), 1_000_000_000_000, dtype=np.int64)
>>> bottleneck.nanmean(a)
1000000022905.4894
>>> np.nanmean(a)
1000000000000.0
``` Thanks @sebasv and @JMBurley for review