At the beginning of my career as a Scrum Master I transitioned, as many others, from a Project Manager position. This is the kind of role where you “own” a team.
You are not part of the team, you “manage” the team: performance reviews, career development, vacations, salary adjustments, all this kind of things.
From one day to another, you have an agile team. Roles are supposed to be functional; titles don’t matter here, right?