Replace example data submodule with subtree

[sethaxen]

Description

As discussed on Slack, this replaces the git submodule approach with including example data in this repo (#2096) with an approach using git subtree. This makes management slightly more complicated on the developer side but makes it easier whenever one needs to download the repo, as special commands are no longer necessary to clone the repo. See https://stackoverflow.com/questions/31769820/differences-between-git-submodule-and-subtree for some comparisons between the two approaches.

Checklist

• Follows official PR format
• New features are properly documented (with an example if appropriate)?
• Changes are listed in changelog

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📚 Documentation preview 📚: https://arviz--2105.org.readthedocs.build/en/2105/

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[sethaxen]

We should document somewhere how developers should update the subtree if arviz_example_data is updated:

$ git subtree pull --prefix arviz/data/example_data https://github.com/arviz-devs/arviz_example_data.git main --squash

Where's a good place for that?

[sethaxen]

@ahartikainen thoughts on this question?

[OriolAbril]

I would say some of the pages in https://python.arviz.org/en/latest/contributing/index.html. Maybe a new one in how-to guides?

[sethaxen]

I would say some of the pages in https://python.arviz.org/en/latest/contributing/index.html. Maybe a new one in how-to guides?

Done! https://arviz--2105.org.readthedocs.build/en/2105/contributing/updating_example_data.html

Unless anything on that page needs to change, this should be ready to merge.