Not sure of the orientation, so I’m going to call what is in the photo the bottom of the door. Given that, do you see any twist in the lower rail (the one in the photo)? Twist in the door? I’m wondering if the rail has twisted and split the stile / mortise. You can try working PVA glue into that gap, but I suspect there is crud in there and deterioration that will affect the bond. Does it even clamp closed cleanly? Is it a big fight or does it squeeze closed easily?
One possible repair would be to go about an inch or two up from the break, saw across the stile and then use your chisel and router plane to fabricate a recess running all the way to the bottom of the door and all the way across the width of the stile. You could stop short of the full width if that fouls a hinge or has some other issue, but it may then be harder to fabricate. Then, glue a piece into that recess so that you have many square inches of fresh, flat wood to form the bond. I would be tempted to take this all the way down (in depth) to the tenon in the lower rail so that you are leveling the tenon cheek (reducing the tenon thickness as little as possible, but ideally all the way across the tenon cheek). The end result is making a laminate with a perfectly fitting, reconstructed mortise and tenon (achieved by the lamination).
This seems a bit risky and if that rail is still twisting, it may just break the door again. There’s no harm in trying to just work glue in there as a first try. If you do that, put a clamp across the work to open and close a zillion times while you force in glue. This can help draw the glue deeper into the crack.