Is working in the field of design considered unlawful (haram), and is it obligatory to abandon this profession if the foundation of learning for it was established using unlicensed software, knowing that the software has now been legally purchased?

You must repent to Allah Almighty for infringing upon the rights of software owners, for intellectual property rights are considered legitimate in Islamic law, and violating them is forbidden. You are obligated to pay the value of the benefits you caused software owners to miss out on, and the damages they incurred, which experts will determine. Pay what is incumbent upon you to the owning entity if you can; otherwise, donate it as charity on their behalf, and strive to pay what will absolve your responsibility. As for the knowledge and work resulting from them, they are permissible, and you are not required to abandon them.