Following layout problems with my document coming from a Tufte-book documentclass, I took into account the new code presented in the following link, which presents the old and the new code: layout problem with \full{\printindex} in Tufte documentclass
I still have two issues that I can't seem to resolve, one of which concerns the layout of the intro pages for the Parts (the other is the subject of a separate question). I would like to have the following format:

Unfortunately, the code relative (see below) to the Part title page formatting in the preamble does not give the same result after using the new code, since the title format is changed, and the text moves on the next page (from page 11 to page 12), from front to back. I get the following result and does not match the desired rendering:

Here is the code which correspond in the preambule to the Part title layout:
% Début Module pour insérer les ornements des parties
\makeatletter
\def\H@old@part[#1]#2{%
\ifnum \c@secnumdepth >-2\relax
\refstepcounter{part}%
\addcontentsline{toc}{part}{\thepart\hspace{1em}#1}%
\else
\addcontentsline{toc}{part}{#1}%
\fi
\markboth{}{}%
{%
\thispagestyle{empty}
\begin{fullwidth}%
\centering
\interlinepenalty \@M
\normalfont
\ifnum \c@secnumdepth >-2\relax
\huge\bfseries \partname\nobreakspace\thepart
\par
\vskip 10\p@
\psvectorian[height=0.2cm]{88}\par
\vskip 10\p@
\fi
\Huge \bfseries #2\par
\end{fullwidth}%
}%
\@endpart}
\makeatother
% Fin Module pour insérer les ornements des parties
How to correct the problem?

\part. If you want a blank page before or after the part page use\cleardoublepagebefore or after. – Simon Dispa Dec 14 '21 at 17:33\documentclassto\end{document}. Just in case: delete all the files generated by the compilation, keeping only the.texand try again. For example, if present, the.auxfile from a former compilation is used. – Simon Dispa Dec 17 '21 at 12:49main.tex. (copy and paste with a new name) – Simon Dispa Dec 17 '21 at 13:51