I can attach files fine in the "advanced editor" view, when the attach option is there. However, if I look at posts and replies in my inbox, then there isn't an attach option.
But, I did find that if I click on the original post title, then it will go to the view where "use advanced editor" is a small link in the top right hand corner, then I can click on that, and then the "attach" option appears in the bottom left. Once you're in the advanced view, then you can do as your screenshots point out, it's getting there that was awkward.
Anyway, I've now attached the project, thanks.