Roles don't -have- attributes.

Hm. The quote was directly from Synopsis 12, so as far as the wording is concerned, you need to argue with the authors.

As far as the semantics are concerned, I did go on to say: "Of course, whatever state they have becomes a part of the instance into which they are composed", so I think we're in tune there.

But, as I also said, and regardless of whether the state is has'd by the Role, or provided by it, that state exists and is presumably usually affected by the Role and persists beyond the invocation of whatever methods the role also provides, so there is no sense in which it can reasonably be described as stateless.

If my limited understanding of ML's Functors means that they are like (my also limited understanding of) Haskell's Typeclasses, then the term composed in the sense you are using it: "composed into"; and that same term in the sense the OP used it: "more easily composable units."; are entirely different things.

With the former composing both operations and state, and the latter performing operations on values only (hence stateless). Quite different beasts. The best discussion I have located upon the difference is this.