Thanks a lot for helping, but I’m not sure that the curvature tool will help me get the result I was hoping for.
I have attached another image indicating the stroke with red. The original artwork is below with black. I guess the original artwork was created with a stroke initially and then being outlined to achieve the same width all along the path.
The issue seems to be where the joins are. They are rounded on the outer part of the joins and sharp on the inner. But I can’t get the inner part to have the same width as the straight line segments.

Hope for more good advice ☺
Thanks