To look like this:
So that the page number is in front of the title of the part and aligned with the other page numbers, and the title of the part is aligned with the part number.
Extra: Is it possible, for example, to have only "Part One" in \sc format?
Here is the code I got so far from other answers:
\documentclass{report}
\usepackage[newparttoc]{titlesec}
\usepackage{titletoc}
\usepackage{titleps}
\usepackage{stackengine}
\usepackage{fmtcount} % For part number in written form
\renewcommand{\thepart}{\Numberstring{part}}
\titleclass{\part}{top}
\titleformat{\part}[display]{\centering\normalfont\large}{\partname>\hspace{4pt}\thepart}{0pt}{\Large}
\titlecontents{part}
[0cm]
{\Large\bfseries\protect\addvspace{15pt}}%
{Part \thecontentslabel\bclap}
{}%
{\enspace\hfill\thecontentspage}%
\begin{document}
\tableofcontents
\part{Title of Part One}
\chapter{chapter}
\section{section}
\part{Title of Part Two}
\chapter{chapter}
\section{section}
\end{document}


