Soul Sculptor and creatures with cast triggers
The dragon will get counters.


  603.10. Normally, objects that exist immediately after an event are checked to see if the event matched any trigger conditions, and continuous effects that exist at that time are used to determine what the trigger conditions are and what the objects involved in the event look like.


To determine if an event (casting a creature spell in this case) triggered any abilities, we look at the state of things immediately after that event occurred. At the time that the game checks to see if anything triggered (immediately after the event), Soul Sculptor's continuous effect has ended.

Note that reverting to a creature when the spell is cast is not a triggered ability, or any ability that uses the stack. For that to be the case, Soul Sculptor would need to be worded as a delayed trigger. Something awkward like "Target creature becomes an enchantment with no abilities. When a creature spell is cast, this effect ends."


  603.7. An effect may create a delayed triggered ability that can do something at a later time. A delayed triggered ability will contain “when,” “whenever,” or “at,” although that word won’t usually begin the ability.


Rather, it is simply a continuous effect that has a limited duration, and when the duration expires, so does the effect.


  611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until the end of the game.


Rule 613 explains how the current values of an object’s characteristics are determined. Immediately after a creature spell has been cast, when the game is determining what the dragon's characteristics are, it determines that the dragon is a creature with its normal abilities, because at that time, the enchantment-changing effect has ended, it is past the stated expiration point of the continuous ability.