I tried to snap to the edge when rotating the plane around the global X axis, but that doesn’t do it parallel and just rotates it as if Ctrl wasn’t pressed down at all. In the transform orientation bound to the edge, it doesn’t work also.
In my case it does it oriented strictly horizontally. Also, if select “Snap With → Center” (before I had Closest), it will do it vertical. The same thing happens with “Edge Center”. In any case I have surely “Affect → Rotate” selected and still ticked “Align Rotation To Target” that doesn’t do anything too.
Hmm, I ocassionally enabled “Align Rotation To Target” and then moved and snapped the plane to the edge along Y axis and that made it perpendicular to that. And then I just rotated by 90 degrees around X axis. It seems this is what I need for. Thanks for help!