Yes, you are correct that scribble has an implication of messy, or at least hurried.
I guess that the meaning of 'jot' is evolving, but I would not use 'jot' to refer to any use of a keyboard, but I would perhaps use it with (say) using a stylus. Jot does sound a little old-fashioned - I don't use it much any more.
'Note' I would use more, and I would use it for a typed digital note.