According to scrum, the scrum master is not the product owner and not a member of the dev team, but rather an objective person who does just the scrum master duties, e.g. facilitating when needed, e.g. making sure people are following scrum instead of getting distracted, not stalled by roadblocks, not taking marching orders from more than one product owner, etc. In scrum, the dev team organizes its time after priorities are set. Scrum does not want a scrum master to be a project manager - if you’ve seen that they’re just mixing unnecessary stuff into scrum and scrum is getting a bad rap for that. I don’t see a scrum master as being a full-time job unless they’re working with multiple teams, so it could easily be anyone knowledgeable outside the team who will objectively play the role.
In my experience, and from what I remember from my own training, the scrum master can very well be part of the team. Having somebody external, objective, well trained, and available exactly when the team needs him looks very good... but pretty difficult to do in practice.
