[Feature]: Add a Universal Search Bar to Podman.io

### Consisely describe the feature.

Seeing the current Podman website, I noticed that there is no search bar. In my view, this is a very important feature for a website, especially for documentation-heavy projects. Most major open-source projects provide a universal search option, and I think Podman could benefit from one as well.

This would become even more useful if the documentation is unified in the near future, as users would have a single place to search across all the available documentation.

For implementing the search, I would highly recommend [Algolia](https://www.algolia.com/). It is one of the leading search-as-a-service platforms and also has an [open-source program](https://www.algolia.com/for-open-source/), which could make it a good fit for an open-source project like Podman.

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### LLM Policy

- [x] This issue is human-written, and folow up comments will also be human-written

Start by reviewing the existing Podman.io website and its documentation layout, then evaluate Algolia as the proposed search service. Define the search scope and integration approach; done means a universal search bar can search the available Podman documentation.

Written by the indexing model from the issue text.