diff --git a/packages/components/CHANGELOG.md b/packages/components/CHANGELOG.md
index 3b8d45be5861bc..5a58ddfda38b99 100644
--- a/packages/components/CHANGELOG.md
+++ b/packages/components/CHANGELOG.md
@@ -66,6 +66,7 @@
 
 ### Internal
 
+-   `DropdownMenu` v2: expose CompositeTypeaheadV2 and CompositeHoverV2 via private APIs ([#64985](https://github.com/WordPress/gutenberg/pull/64985)).
 -   `DropdownMenu` v2: fix flashing menu item styles when using keyboard ([#64873](https://github.com/WordPress/gutenberg/pull/64873), [#64942](https://github.com/WordPress/gutenberg/pull/64942)).
 -   `DropdownMenu` v2: refactor to overloaded naming convention ([#64654](https://github.com/WordPress/gutenberg/pull/64654)).
 -   `DropdownMenu` v2: add `GroupLabel` subcomponent ([#64854](https://github.com/WordPress/gutenberg/pull/64854)).
diff --git a/packages/components/src/private-apis.ts b/packages/components/src/private-apis.ts
index fa9fece048617e..7bcab0e052e022 100644
--- a/packages/components/src/private-apis.ts
+++ b/packages/components/src/private-apis.ts
@@ -18,6 +18,8 @@ lock( privateApis, {
 	CompositeGroupV2: Composite.Group,
 	CompositeItemV2: Composite.Item,
 	CompositeRowV2: Composite.Row,
+	CompositeTypeaheadV2: Composite.Typeahead,
+	CompositeHoverV2: Composite.Hover,
 	useCompositeStoreV2: useCompositeStore,
 	__experimentalPopoverLegacyPositionToPlacement,
 	createPrivateSlotFill,
diff --git a/packages/dataviews/src/components/dataviews-filters/search-widget.tsx b/packages/dataviews/src/components/dataviews-filters/search-widget.tsx
index 1b369222b8f28c..24ef3b5594b413 100644
--- a/packages/dataviews/src/components/dataviews-filters/search-widget.tsx
+++ b/packages/dataviews/src/components/dataviews-filters/search-widget.tsx
@@ -8,6 +8,7 @@ import removeAccents from 'remove-accents';
 /**
  * WordPress dependencies
  */
+import { useInstanceId } from '@wordpress/compose';
 import { __, sprintf } from '@wordpress/i18n';
 import { useState, useMemo, useDeferredValue } from '@wordpress/element';
 import {
@@ -27,7 +28,8 @@ import type { Filter, NormalizedFilter, View } from '../../types';
 const {
 	CompositeV2: Composite,
 	CompositeItemV2: CompositeItem,
-	useCompositeStoreV2: useCompositeStore,
+	CompositeHoverV2: CompositeHover,
+	CompositeTypeaheadV2: CompositeTypeahead,
 } = unlock( componentsPrivateApis );
 
 interface SearchWidgetProps {
@@ -84,22 +86,37 @@ const getNewValue = (
 	return [ value ];
 };
 
+function generateFilterElementCompositeItemId(
+	prefix: string,
+	filterElementValue: string
+) {
+	return `${ prefix }-${ filterElementValue }`;
+}
+
 function ListBox( { view, filter, onChangeView }: SearchWidgetProps ) {
-	const compositeStore = useCompositeStore( {
-		virtualFocus: true,
-		focusLoop: true,
-		// When we have no or just one operator, we can set the first item as active.
-		// We do that by passing `undefined` to `defaultActiveId`. Otherwise, we set it to `null`,
-		// so the first item is not selected, since the focus is on the operators control.
-		defaultActiveId: filter.operators?.length === 1 ? undefined : null,
-	} );
+	const baseId = useInstanceId( ListBox, 'dataviews-filter-list-box' );
+
+	const [ activeCompositeId, setActiveCompositeId ] = useState<
+		string | null | undefined
+	>(
+		// When there are one or less operators, the first item is set as active
+		// (by setting the initial `activeId` to `undefined`).
+		// With 2 or more operators, the focus is moved on the operators control
+		// (by setting the initial `activeId` to `null`), meaning that there won't
+		// be an active item initially. Focus is then managed via the
+		// `onFocusVisible` callback.
+		filter.operators?.length === 1 ? undefined : null
+	);
 	const currentFilter = view.filters?.find(
 		( f ) => f.field === filter.field
 	);
 	const currentValue = getCurrentValue( filter, currentFilter );
 	return (
 		<Composite
-			store={ compositeStore }
+			virtualFocus
+			focusLoop
+			activeId={ activeCompositeId }
+			setActiveId={ setActiveCompositeId }
 			role="listbox"
 			className="dataviews-filters__search-widget-listbox"
 			aria-label={ sprintf(
@@ -108,18 +125,29 @@ function ListBox( { view, filter, onChangeView }: SearchWidgetProps ) {
 				filter.name
 			) }
 			onFocusVisible={ () => {
-				if ( ! compositeStore.getState().activeId ) {
-					compositeStore.move( compositeStore.first() );
+				// `onFocusVisible` needs the `Composite` component to be focusable,
+				// which is implicitly achieved via the `virtualFocus: true` option
+				// in the `useCompositeStore` hook.
+				if ( ! activeCompositeId && filter.elements.length ) {
+					setActiveCompositeId(
+						generateFilterElementCompositeItemId(
+							baseId,
+							filter.elements[ 0 ].value
+						)
+					);
 				}
 			} }
-			render={ <Ariakit.CompositeTypeahead store={ compositeStore } /> }
+			render={ <CompositeTypeahead /> }
 		>
 			{ filter.elements.map( ( element ) => (
-				<Ariakit.CompositeHover
-					store={ compositeStore }
+				<CompositeHover
 					key={ element.value }
 					render={
 						<CompositeItem
+							id={ generateFilterElementCompositeItemId(
+								baseId,
+								element.value
+							) }
 							render={
 								<div
 									aria-label={ element.label }
@@ -185,7 +213,7 @@ function ListBox( { view, filter, onChangeView }: SearchWidgetProps ) {
 							) }
 					</span>
 					<span>{ element.label }</span>
-				</Ariakit.CompositeHover>
+				</CompositeHover>
 			) ) }
 		</Composite>
 	);