I’m really glad you asked because there’s some gold in this thread about it Tool to auto-generate model diagrams? - #14 by betanalpha.
I would definitely welcome more info on this especially from @Bob_Carpenter and @betanalpha, two from that linked thread. You may be exactly right about sufficiency, so Stan can infer all things DAG but the thing with sufficiency is that it sounds like Stan can infer things non-DAG, or not very faithfully represented by a DAG.