Should sidebar "Search categories" filter be a SearchControl?

[mirka]

What problem does this address?

The "Search categories" field in the Post sidebar uses a normal TextControl even though it's a search field.

gutenberg/packages/editor/src/components/post-taxonomies/hierarchical-term-selector.js

Lines 409 to 416 in 8169dfd

	<TextControl
	// TODO: Switch to `true` (40px size) if possible
	__next40pxDefaultSize={ false }
	__nextHasNoMarginBottom
	label={ filterLabel }
	value={ filterValue }
	onChange={ setFilter }
	/>

What is your proposed solution?

@WordPress/gutenberg-design Should this be replaced with the SearchControl component, so it can signal that it's a search field, both visually and semantically? At the very least we should probably add back the type="search" attribute that seems to have been there in the past.

[jasmussen]

I'd think so.