It would be hard to reach out and not have it come across as you thinking they stole the idea and/or you are bitter about not being hired. If you think you can do that in a “hey hit me up as a consultant or if you have any more open roles” type of way then maybe a casual message to the CTO.
Did they actually hire someone for that role? Is it possible their growth strategy isn’t based on the idea but is something else? Do they have competitors that might also be interested in this vague idea? edit: I assume you didn’t sign an NDA for an interview.