I am also an ex-shoulder problem person, and even though it’s been many years, I still have to be careful with what I do, particularly how much resistance I use.
The PT exercises are your first line of defense but progression after that really depends on the person and the degree of the injury. With shoulders there is a fine line between too much and too little. While the rotator cuff is often the victim, the cause of the injury (except for trauma) is often faulty posture over time. It is often the entire shoulder girdle that is unstable.
The core exercises I would watch carefully are planks and even something as seemingly as bird dog because they can show you how unstable the shoulder girdle really is.