Responsibility of scrum master
We are new to scrum and team with most are experience devs. (even decades). The project manager (experience dev but new to project management) gave a scrum master role to a junior BA. She is ambitious well organized and not much scrum or even matured working experience. She seems to eating into PM role are and becoming bossy type. May be she thinks her responsible is to make project successful in-expense of what others do or thinks.
With real agile experience with 3/4 years (another organization) ,I feel those agile projects were more democratic and encourage autonomy. How could I bring-up that we are going in a wrong way?
There are actually two questions here:
What went wrong?
From the short description, it seems that there has been no training but the person was just given the job title (maybe with a copy of the scrum guide). SM is a demanding role which has to be learned and which requires exquisite interpersonal skills, it's not just about holding ceremonies and pushing the project forward.
What can you do to help fix it?
How you could bring it up and help your organization improve depends largely on your organization's communication culture and on the relationship between you, the project manager, and the scrum master. I'd try to be open but non-aggressive in my communication, but many people tend to enter a defensive position when you point out problems to them, so this won't always work easily. You could concentrate on common goals (project success, team performance) and point out which changes could help to secure these goals, that is, focus on positive suggestions instead of criticism.