These options store ID values, you just need to get the ID value from the ACF field, this can be done by not getting the formatted value using false for the 3rd argument of get_field()
update_option('custom_logo',get_field('platform_logo','options', false), true); // Update Site Logo
update_option('site_icon',get_field('platform_favicon','options', false), true); // Update Site Favicon / Icon
