What is a safe and healthy way to handle breaking away from parents who are overly dependent on me without losing a relationship with them?

Let them know what are your plans and why are you doing it. Explain to them that this does not change who they are and what they mean to you.

Shift. Shift away from them if your parents are too dependent on you but you don't want to hurt them. Tell them any other reason for he shift. Don't forget to send them occasional gifts and cards to show you love them but don't be in a very close contact with then that they can trouble you even from a distance.

Make them understand that you have selected your life's path and want to achieve something for yourself but be grateful to them for helping you through all these years

It takes a toll no matter what you do. And detachment takes a toll. On both sides. But mostly on those who are more attached to the relationship, to the close relationship. In your case, the parents. As I see it, when a separation is unavoidable or needed, Best way is to start from current frequency of interactions, close interactions. Then slowly decrease the frequency. Abrupt separation will not help anyone. That's the best way from multiple points of view. But the most important point of view, is the habit point of view. Habit need very strict rhythm, to happen rhythmically, sequence. Has to. Otherwise, habit gets weakened. Like, if you don't accelerate the car, it's already stopping, slowly, but surely. So, to minimize the pain of detachment, while the habit of attachment is weakened, best way is to decrease the frequency, in a planned way. Like next month, I will interact number-1 where number = current number of interactions. and keep decreasing until balance is reached.