In my personal experience, typing my thoughts when I am working through creative problems seem to help. But it's subjective and would like to have some confirmation.
Atkin in "The Phenomenological Influence of Inner Speech on Executive" shows that Thinking Out Loud can help in one problem-solving exercise. It seems that it was first noted by Newell and Simon in 1972 in their book.
(this is also confirmed anecdotally in Rubber Duck Debugging in programming, which for some works while typing)
There is a lot of literature connected to writing for learning, in school settings, so I am not sure if this works for creative problems or mostly for integrating knowledge.
There is also idea of "freewriting" by Peter Elbow which is something similar to what I mean, but it seems his research and articles that cite him focus on freewriting for writing fiction (I guess it's a bit similar).
Regarding phrasing, I saw phrases used as inner speech writing and private writing, but it doesn't seem to return a lot of results.
Sorry if I am breaking any rules here, I am not a student of psychology just a hobbyist