Set the search state in the interactivity state for inherited queries.

packages/block-library/src/search/index.php

@@ -107,7 +107,7 @@ function render_block_core_search( $attributes, $content, $block ) {
 			wp_enqueue_script_module( '@wordpress/block-library/search/view' );
 
 			if ( $instant_search_enabled ) {
-				$input->set_attribute( 'data-wp-bind--value', 'context.search' );
+				$input->set_attribute( 'data-wp-bind--value', 'state.searchGetter' );
 				$input->set_attribute( 'data-wp-on-async--input', 'actions.updateSearch' );
 			}
 		}
@@ -238,6 +238,10 @@ function render_block_core_search( $attributes, $content, $block ) {
 		// If the query is defined in the URL, it overrides the block context value.
 		$search = empty( $_GET[ $search_key ] ) ? $search : sanitize_text_field( $_GET[ $search_key ] );
 
+		if ( $is_inherited ) {
+			wp_interactivity_state( 'core/search', array( 'search' => $search ) );
+		}
+
 		$form_context = array_merge(
 			$form_context,
 			array(

packages/block-library/src/search/view.js

@@ -48,6 +48,10 @@ const { state, actions } = store(
 				}
 				return ctx.isSearchInputVisible;
 			},
+			get searchGetter() {
+				const { isInherited, search } = getContext();
+				return isInherited ? state.search : search;
+			},
 		},
 		actions: {
 			openSearchInput( event ) {
@@ -88,14 +92,18 @@ const { state, actions } = store(
 			*updateSearch( e ) {
 				const { value } = e.target;
 
-				const ctx = getContext();
-
 				// Don't navigate if the search didn't really change.
-				if ( value === ctx.search ) {
+				if ( value === state.searchGetter ) {
 					return;
 				}
 
-				ctx.search = value;
+				const ctx = getContext();
+
+				if ( ctx.isInherited ) {
+					state.search = value;
+				} else {
+					ctx.search = value;
+				}
 
 				// Debounce the search by 300ms to prevent multiple navigations.
 				supersedePreviousSearch?.();