Update search box design in the documentation

[sdispater]

This a slight redesign of the search box in the documentation that condenses a bit more the result list ensuring that the Algolia logo is a bit more visible.

The Algolia logo has also been updated to use the most recent one.

[github-actions[bot]]

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[Secrus]

The color of the Algolia logo seems to have contrast issues in dark mode. Shall it remain as it is (kinda hard to read if you ask me) or will you adjust it (or maybe it could change color to white/light gray in dark mode?)?