Use Mamba in Azure CI
Use Mamba in Azure CI to save ~10 minutes of setup time.

- [ ] closes #xxxx (Replace xxxx with the Github issue number)
- [ ] [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
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

ping @mroeschke  Did mamba solve unpinned dependencies differently than conda for builds in Azure?

For example in GHA builds, I noticed mamba would install pyarrow=2 while conda would install pyarrow=6 It seems like it always installs Arrow 6, so no change in version.

Edit: Ran a diff of all versions, no changes except for build numbers which are due to different start times I am assuming. @jonashaag please don't force push after an approval. @simonjayhawkins Thanks, will keep that in mind in the future. In this case it was a rebase to latest `main` using the GitHub UI. Hmm, seems like there is a problem with Azure and Mamba, see https://github.com/mamba-org/mamba/issues/488

```
    RuntimeError: Operation not permitted: '/usr/local/miniconda/pkgs/cache/dd44a73b.json'

``` > Hmm, seems like there is a problem with Azure and Mamba, see [mamba-org/mamba#488](https://github.com/mamba-org/mamba/issues/488)
> 
> ```
>     RuntimeError: Operation not permitted: '/usr/local/miniconda/pkgs/cache/dd44a73b.json'
> ```

Is this a full blocker for implementing this? Let's try the workaround suggested there. This seems to fix the issue, although I'm not sure if will reappear. The other repos that have this implemented successfully for some time indicate that it's not the case but I don't feel confident about that. thanks @jonashaag very nice! @meeseeksdev backport 1.4.x Something went wrong ... Please have a look at my logs.