Enable search as you type and remove sidebar search

[TimMonko]

References and relevant issues

Closes #979

Description

This removes the sidebar search to enable search-as-you-type functionality in the navbar search.
The functionality needs the newest release of napari-sphinx-theme so if you build locally make sure to use pixi update.
😁

I want to follow-this up to potentially improve the visual of the search bar

[psobolewskiPhD]

Oh wow, this made me notice that the search/mag glass in the nav bar doesn't work on live napari.org ?!?

[TimMonko]

Oh wow, this made me notice that the search/mag glass in the nav bar doesn't work on live napari.org ?!?

Can you check again? It should pop-up a modal on the homepage, on the other pages its sneakier though, focus snaps to the sidebar search (which is part of the motivation of this change)

[psobolewskiPhD]

focus snaps to the sidebar search (which is part of the motivation of this change)

Oh, I guess i didn't notice.
Since nothing happens I assumed it was broken. So it's not broken broken, but certainly not a good experience.

[TimMonko]

Themeing follow-up napari/napari-sphinx-theme#223
If we like this, I will make a napari/docs follow-up to use the search-field for the navbar rather than the search-symbol as it is now (so its a field when screen is wide and just a symbol when narrow)