Update after chat with RJ in Sales. He says, “So, forms was a Business feature but its rolling out to the Premium tier. It should be fully available on the 17th.”
Asana documentation at Create Forms in Asana | Product Guide • Asana Product Guide says that Forms are available to Premium accounts:
I have a Premium account. When I try to access forms, I see this [“Upgrade to Business”]:
Which is it?
I was about to make the announcement, but you’ve been quicker 
We’re rolling this update progressively (it was just enabled today to 25% of our users) but it will soon be available to every Premium users, so don’t worry it will soon be available to you too! Watch out for an announcement with all details later today!