Consider adding a search icon to the Geologist + Zoologist footers

[kjellr]

Let's try adding a search to the footer of Geologist + Zoologist. It should:

• Use var(--wp--custom--font-sizes--tiny) text (We might need a block style to accomplish this, since we don't want that to apply to all search blocks).
• Have half of the normal var(--wp--custom--form--padding) around the input field.
• Be the width of the content column.
• Only be available on the archive pages, on single post/pages.

I think we should give this a try in a PR and see what we think. To avoid messing with folks' live sites, we may need to implement this in a way that doesn't add it to existing non-FSE sites.

Mockup:

[MaggieCabrera]

I think we could consider making a block style on Blockbase for a small version of the search block, since we usually have a big one on the search page/404 and having a smaller one on the header/footer is common too.

It's important to consider that the search block font size rules changed recently (they weren't working on theme.json correctly before) and maybe our current rules need a bit of adjusting so this would be a good opportunity to revisit that.