Update algolia docsearch component to V3

[LachlanCourt]

Several dramas with the existing docsearch component lead to me starting investigation around updating it a LONG time ago, I finally got around to finishing it today 🎉 It looks a little bit different but I've tried to match the styles as closely as possible, this is totally open to feedback, I was trying to juggle minimal customisations vs looking nice so let me know if you think something looks off and if you have any suggestions :)

Preview

Note that the links that will show up in the search will link to the active site, not back to the preview so if you are clicking around just make sure you keep an eye on the URL. Pls also consider checking on different screen sizes, mobile, tablet etc

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[ysims]

Looks good on mobile. On desktop I noticed the colour of the background when the search is clicked is blue-ish. I feel like a grey would be better, particularly when in dark mode.

[LachlanCourt]

What part of the search are you clicking sorry @ysims ? I don't seem to be able to reproduce 🤔

[ysims]

@LachlanCourt

Outside of the search box, the rest of the site gets a blue-grey overlay.

[LachlanCourt]

Have updated to a light grey now instead, lemme know what you think @ysims

[ysims]

Looks good!