According to this site for $args to use https://www.billerickson.net/code/wp_query-arguments/
'meta_query' => array( //(array) - Custom field parameters (available with Version 3.1).
array(
'key' => 'color', //(string) - Custom field key.
'value' => 'blue', //(string/array) - Custom field value (Note: Array support is limited to a compare value of 'IN', 'NOT IN', 'BETWEEN', or 'NOT BETWEEN')
'type' => 'CHAR', //(string) - Custom field type. Possible values are 'NUMERIC', 'BINARY', 'CHAR', 'DATE', 'DATETIME', 'DECIMAL', 'SIGNED', 'TIME', 'UNSIGNED'. Default value is 'CHAR'.
'compare' => '=', //(string) - Operator to test. Possible values are '=', '!=', '>', '>=', '<', '<=', 'LIKE', 'NOT LIKE', 'IN', 'NOT IN', 'BETWEEN', 'NOT BETWEEN'. Default value is '='.
),
array(
'key' => 'price',
'value' => array( 1,200 ),
'compare' => 'NOT LIKE'
)
So following the above example I would maybe try something like this and add as many keys as you need to in order to search all the taxonomies you want.
$args['meta_query'] = array(
array(
'key' => my_key_1,
'value' => $args['s'],
'compare' => 'LIKE',
),
array(
'key' => my_key_2,
'value' => $args['s'],
'compare' => 'LIKE',
),
array(
'key' => my_key_3,
'value' => $args['s'],
'compare' => 'LIKE',
)
);
return $args;
