Solution:
After several hours of meddling with different documentation and APIs, here’s the solution that worked for me.
add_filter('woocommerce_rest_product_object_query', function(array $args, \WP_REST_Request $request) {
$modified_after = $request->get_param('modified_after');
if (!$modified_after) {
return $args;
}
$args['date_query'][0]['column'] = 'post_modified';
$args['date_query'][0]['after'] = $modified_after;
return $args;
}, 10, 2);
It’s to be noted that this is for version v3 (latest when this answer is written) and it may or may not work for the previous versions.