Keep the stick a bit forward all the time. Push it further forward before beginning to bank left, then use left rudder to keep the nose down when the turning circle tightens, and the plane's roll angle gets steeper.
For a right turn pull the stick slightly back after (!) banking with the ailerons. The more steep the angle gets (more banking - ailerons, and pulling - elevator), the more left rudder you can apply to keep the nose pointing at the horizon. Always use a reference like clouds or the horizon for your heading, and elevation. Due to the rotary you need left rudder for either turn. When in combat, use one hand for the keyboard gun trigger, and keep the other reserved for your joystick input.
While practicing, make only small inputs. Use your fingertips only to rotate the stick for rudder input (without pedals).
It is just when you move a real stick to the right for maybe 20", your joystick does that with 1/2". It is "a bit sensitive", but that's what the Dr.I is all about. You will get used to it

Albatros pilots hated the Dr.I until they knew how to fly it.
But then I still think the Albatros is a bit more elegant lol
The Dr.I is easier to fly than the Camel and really more good-mooded, but the controls are a bit more "to the point" (I even think it still is too clumsy regarding flying sideways). I have been to a museum today and had a look at the Dr.I - there is no way comparing it to a Sopwith tripe, it is much more "compact" and sturdy. You almost "see" its capabilities, cantilever wings, no wires and this thing is SHORT.
Greetings,
Catfish