Native timestamp on wp_options option

There’s no “updated” column in the wp_options table.

mysql> describe wp_options;
+--------------+-----------------+------+-----+---------+----------------+
| Field        | Type            | Null | Key | Default | Extra          |
+--------------+-----------------+------+-----+---------+----------------+
| option_id    | bigint unsigned | NO   | PRI | NULL    | auto_increment |
| option_name  | varchar(191)    | NO   | UNI |         |                |
| option_value | longtext        | NO   |     | NULL    |                |
| autoload     | varchar(20)     | NO   | MUL | yes     |                |
+--------------+-----------------+------+-----+---------+----------------+
4 rows in set (0.07 sec)

If you need to know when an option was updated, you’ll need to inject that information into the option itself. If you’re managing the code, it’s easy enough: just add a new field to the array that you’re saving.

eg:

update_option(
    'instagram',
    array(
        'username' => 'semirtravels',
        'user_id'  => '{your user ID}',
        // ...
        'last_updated' => time(),
   )
);

If not, you might be able to intercept it using the pre_update_option_{$option} filter hook:

add_filter( 'pre_update_option_instagram', 'wpse_400857_add_updated_time', 10, 3 );
/**
 * Adds the current time() to the value of the `instagram` option.
 *
 * @param  mixed  $value     The option's value.
 * @param  mixed  $old_value The option's previous value.
 * @param  string $option    The option name.
 * @return mixed             The filtered option value.
 */ 
function wpse_400857_add_updated_time( $value, $old_value, $option ) {
    $value['last_updated'] = time();
    return $value;
}