Project management is quite often a major task of the team managers, especially if they span across multiple teams. You need to budget for the teams, arrange fo

Project management is quite often a major task of the team managers, especially if they span across multiple teams. You need to budget for the teams, arrange for the work to be roughly scoped further in the future than one or two sprints. You also need to balance things if e.g. new people are hired, or teams are split etc. You are not an individual contributor anymore. Of course you can have the team lead do that, but they will quit in a month because they no longer have any time to write code or spend with the team.