Would you say from experience, either task or relationship leadership style works better for DevOps? Or would you go for something else in this context than Forsyth's theory?
Different types of leadership styles are required. To start with DevOps in a company, one has to apply a different leadership style compared to when it has already been implemented.
When one starts with DevOps a cultural change has to be done and engineers should get rid of, for example, the "throw it over the wall" mindset. When DevOps has been implemented, a leader should be able to communicate well with other teams to connect multiple departments in a company.
In summary, in the beginning a leadership style that motivates people to implement DevOps is required. Later communication between teams and how the team will work in the organization, i.e. more focus on external.
A leadership style that could be used to implement DevOps is a transformational leadership style.