docs: use `mike` for docs infra

### Feature Request / Improvement

Follow up to #14267, we made improvements to the local preview experience by only rendering the most recent docs. This is done in a manual fashion using the build scripts.

I want to explore using [`mike`](https://github.com/jimporter/mike) for building versioned docs. Mike can potentially help with versioning and rendering; we do this today manually.

This is somewhat of a big change and we should explore breaking down the tasks. We should be very careful not to break https://iceberg.apache.org/

### Query engine

None

### Willingness to contribute

- [x] I can contribute this improvement/feature independently
- [x] I would be willing to contribute this improvement/feature with guidance from the Iceberg community
- [ ] I cannot contribute this improvement/feature at this time

Start by reviewing the existing build scripts and the changes from issue #14267, then compare their manual version rendering with mike. Break the exploration into smaller tasks and verify that the resulting versioned docs workflow preserves iceberg.apache.org; done means the docs can be built and previewed without regressions.

Written by the indexing model from the issue text.