Is the Hajj of one who performs it with a free campaign, commissioned by the campaign owner to supervise the pilgrims, accepted? And what is the ruling on that?

Your Hajj is valid. However, your joining the campaign and benefiting from its services without the owner's permission is impermissible. You must inform the campaign owner about this. Then, either he forgives you, or you pay him for your Hajj. You must also repent for what you have done.