They can be used interchangeably but they do hold different meaning. “Essere da solo” means “Being alone” while “Stare da solo” also has a connotation of “staying” as in “staying still” so the emphasis is a bit different.
Let’s see a few examples:
- Sto da solo in auto. (I’m staying alone in my car.)
- Sono da solo in auto. (I am alone in my car.)
Both of these sentences have the same meaning but the emphasis is different (“Sto da solo in auto” emphasizes the act of staying in the car while “Sono da solo in auto” the state of being alone.)
There are a few cases in which there is a more significant difference in meaning:
- A pranzo sono solo.
- A pranzo sto da solo.
Both sentences mean “I am alone at lunch”, but in the first case the person most likely doesn’t enjoy being alone, while in the second case the person most likely chooses to be alone.
I hope I cleared your doubts :)