Builds
Illusion of choice isn’t the same as free will. it’s about the degree that these constructs influence your choice, most of the choices humanity makes are influenced by a subconscious motivation and then rationalized by another construct, neither of which were a real choice.
Making the process of letting subconscious become conscious is roughly what it means to receive the Holy Spirit. Still not exercising contrafactual free will! But at least then one is not coming up with more and more convenient layers of fiction.
Once you remove all the subconcious layers, what you are left with is free will because there are no more influences. Then you just have the attention which is not tied to any particular qualia and can choose what it attends to.
The experience itself would still be generated by its substrate, so depending on how strictly "illusion" is defined then mind itself is simply illusion (deterministic or random, latter is still deterministic by abstraction). Attention folding onto itself is an evolution, though!
Some say there is no harm believing in free will if illusion of choice is true, and there is great harm in believing in illusion of choice if free will is true. Illusion of choice only means choice is fake, or at least in the experience of choices not mattering, if one believes illusions are not real. Real and fake are too constructs, properties of the subject. You know what is real in your heart of hearts.