I've never done this before, but I was just looking through the framework code as I was curious.
The Illuminate\Mail\MailServiceProvider registers a singleton MailManager and a Mailer which is built by the MailManager. Since this already exists in the container and has read the config settings by the time it gets to your code, changing the config settings doesn't do anything.
You will need to create a new Mailer for the vendor. And looking through the Notifications documentation, you can customise the mailer being used:
public function toMail(object $notifiable): MailMessage
{
return (new MailMessage)
->mailer('postmark')
->line('...');
}
So instead of postmark you would use the Mailer class that you create for your vendor.
As I said, I've never done it before and this is all theory. Hopefully it points you in the right direction.