“Can there be an executive without a state?” An excellent and fundamental question. Inasmuch as an institution “does,” in theory, the executive would be the part that is “doing.” I think.
The legislative from Sinai idea is that the law is divinely originated, not man-made. While we still inherently (must) have a power to interpret, the power to enact, these days, is not clear, and would only be within the rigid rubric from Sinai.
Involved laypersons would be the non-rabbis, who are trying to act upon the rabbinic interpretation of the laws from Sinai and regulations added thereafter.
Obviously this is a whimsical and theoretical discussion. But aren’t these fundamental structures important to define?