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. If one would like to start with DevOps in a company one has to apply a different leadership style then when it is already implemented.
When one starts with DevOps a cultural change has to be done and engineers should get ride of for example the "through 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.
Healthy DevOps teams tend to be relatively small and relatively independent when they work really well. If you have a team like this, then task oriented leadership will work well because it fits nicely with the general DevOps philosophy.