You haven’t actually given the context. Presumably both of these people are songwriters.
“Writ out” is not standard English, but the meaning is clear. To be all [verb]-ed out is a common construction, indicating that you’ve had more than enough of a certain activity and just can’t do it any more, at least for the time being.
Here, of course, he’s all “written out” (but he can’t say that because it means something else!).
