diff --git a/src/wp-includes/block-template-utils.php b/src/wp-includes/block-template-utils.php
index 065cfcc037..98c151048a 100644
--- a/src/wp-includes/block-template-utils.php
+++ b/src/wp-includes/block-template-utils.php
@@ -490,36 +490,21 @@ function _inject_theme_attribute_in_template_part_block( &$block ) {
 }
 
 /**
- * Parses a block template and removes the theme attribute from each template part.
+ * Removes the `theme` attribute from a given template part block.
  *
- * @since 5.9.0
+ * @since 6.4.0
  * @access private
  *
- * @param string $template_content Serialized block template content.
- * @return string Updated block template content.
+ * @param array $block a parsed block.
+ * @return void
  */
-function _remove_theme_attribute_in_block_template_content( $template_content ) {
-	$has_updated_content = false;
-	$new_content         = '';
-	$template_blocks     = parse_blocks( $template_content );
-
-	$blocks = _flatten_blocks( $template_blocks );
-	foreach ( $blocks as $key => $block ) {
-		if ( 'core/template-part' === $block['blockName'] && isset( $block['attrs']['theme'] ) ) {
-			unset( $blocks[ $key ]['attrs']['theme'] );
-			$has_updated_content = true;
-		}
+function _remove_theme_attribute_from_template_part_block( &$block ) {
+	if (
+		'core/template-part' === $block['blockName'] &&
+		isset( $block['attrs']['theme'] )
+	) {
+		unset( $block['attrs']['theme'] );
 	}
-
-	if ( ! $has_updated_content ) {
-		return $template_content;
-	}
-
-	foreach ( $template_blocks as $block ) {
-		$new_content .= serialize_block( $block );
-	}
-
-	return $new_content;
 }
 
 /**
@@ -1278,7 +1263,10 @@ function wp_generate_block_templates_export_file() {
 	// Load templates into the zip file.
 	$templates = get_block_templates();
 	foreach ( $templates as $template ) {
-		$template->content = _remove_theme_attribute_in_block_template_content( $template->content );
+		$template->content = traverse_and_serialize_blocks(
+			parse_blocks( $template->content ),
+			'_remove_theme_attribute_from_template_part_block'
+		);
 
 		$zip->addFromString(
 			'templates/' . $template->slug . '.html',
diff --git a/src/wp-includes/deprecated.php b/src/wp-includes/deprecated.php
index 0375d69b4f..9f8981d663 100644
--- a/src/wp-includes/deprecated.php
+++ b/src/wp-includes/deprecated.php
@@ -6084,3 +6084,43 @@ function _inject_theme_attribute_in_block_template_content( $template_content )
 
 	return $template_content;
 }
+
+/**
+ * Parses a block template and removes the theme attribute from each template part.
+ *
+ * @since 5.9.0
+ * @deprecated 6.4.0 Use traverse_and_serialize_blocks( parse_blocks( $template_content ), '_remove_theme_attribute_from_template_part_block' ) instead.
+ * @access private
+ *
+ * @param string $template_content Serialized block template content.
+ * @return string Updated block template content.
+ */
+function _remove_theme_attribute_in_block_template_content( $template_content ) {
+	_deprecated_function(
+		__FUNCTION__,
+		'6.4.0',
+		'traverse_and_serialize_blocks( parse_blocks( $template_content ), "_remove_theme_attribute_from_template_part_block" )'
+	);
+
+	$has_updated_content = false;
+	$new_content         = '';
+	$template_blocks     = parse_blocks( $template_content );
+
+	$blocks = _flatten_blocks( $template_blocks );
+	foreach ( $blocks as $key => $block ) {
+		if ( 'core/template-part' === $block['blockName'] && isset( $block['attrs']['theme'] ) ) {
+			unset( $blocks[ $key ]['attrs']['theme'] );
+			$has_updated_content = true;
+		}
+	}
+
+	if ( ! $has_updated_content ) {
+		return $template_content;
+	}
+
+	foreach ( $template_blocks as $block ) {
+		$new_content .= serialize_block( $block );
+	}
+
+	return $new_content;
+}
diff --git a/tests/phpunit/tests/block-template-utils.php b/tests/phpunit/tests/block-template-utils.php
index e5d4a7cdc8..b06e931529 100644
--- a/tests/phpunit/tests/block-template-utils.php
+++ b/tests/phpunit/tests/block-template-utils.php
@@ -361,13 +361,39 @@ class Tests_Block_Template_Utils extends WP_UnitTestCase {
 
 	/**
 	 * @ticket 54448
+	 * @ticket 59460
 	 *
 	 * @dataProvider data_remove_theme_attribute_in_block_template_content
+	 *
+	 * @expectedDeprecated _remove_theme_attribute_in_block_template_content
 	 */
 	public function test_remove_theme_attribute_in_block_template_content( $template_content, $expected ) {
 		$this->assertSame( $expected, _remove_theme_attribute_in_block_template_content( $template_content ) );
 	}
 
+	/**
+	 * @ticket 59460
+	 *
+	 * @covers ::_remove_theme_attribute_from_template_part_block
+	 * @covers ::traverse_and_serialize_blocks
+	 *
+	 * @dataProvider data_remove_theme_attribute_in_block_template_content
+	 *
+	 * @param string $template_content The template markup.
+	 * @param string $expected         The expected markup after removing the theme attribute from Template Part blocks.
+	 */
+	public function test_remove_theme_attribute_from_template_part_block( $template_content, $expected ) {
+		$template_content_parsed_blocks = parse_blocks( $template_content );
+
+		$this->assertSame(
+			$expected,
+			traverse_and_serialize_blocks(
+				$template_content_parsed_blocks,
+				'_remove_theme_attribute_from_template_part_block'
+			)
+		);
+	}
+
 	public function data_remove_theme_attribute_in_block_template_content() {
 		return array(
 			array(