Add custom part name to header using kaobook template in LaTeX

[DanielWicz]

I am using the kaobook template for my document in LaTeX, and I would like to add the custom part name to the header. By default, the header only shows the chapter name. How can I modify the kaobook template to include the part name in the header, and how can I update it when using the \addpart command ?

I see that kaobook defines headers in the kao.sty as:

% Header style with chapter number, chapter title, and page in the header (used throughout the document)
\renewpagestyle{scrheadings}{%
	{\smash{\hspace{-\headmarginparwidth}\hspace{-\headmarginparsep}\makebox[\headtotal][l]{%
		\makebox[7\hscale][r]{\thepage}%
		\makebox[3\hscale]{}\rule[-1mm]{0.5pt}{19\vscale-1mm}\makebox[3\hscale]{}%
		\makebox[\headtextwidth][l]{\leftmark}}}}%
	{\smash{\makebox[0pt][l]{\makebox[\headtotal][r]{%
		\makebox[\headtextwidth][r]{\hfill\rightmark}%
		\makebox[3\hscale]{}\rule[-1mm]{0.5pt}{19\vscale-1mm}\makebox[3\hscale]{}%
		\makebox[7\hscale][l]{\thepage}}}}}%
	{\smash{\makebox[0pt][l]{\makebox[\headtotal][r]{%
		\makebox[\headtextwidth][r]{\hfill\rightmark}%
		\makebox[3\hscale]{}\rule[-1mm]{0.5pt}{19\vscale-1mm}\makebox[3\hscale]{}%
		\makebox[7\hscale][l]{\thepage}}}}}%
}{%
	{}%
	{}%
	{}%
}

How to modify it, so that part can be displayed in the header ?