Microsoft has said that it plans to bring sync to Edge-Linux, but has not provided a timetable for that essential feature. Without MSA sign-in and sync, Edge-Linux is not useful for end users. Edge-Linux at this point is intended for testing and use by developers, not end users. MSA sign-in and Sync will probably be in place before a Stable version is released.
No one outside Microsoft has any idea when that might be. We will just have to be patient.