Convert final appendix to a supplementary material section

Please try the below given

\documentclass{report}
\usepackage[toc,page,titletoc]{appendix}
\usepackage[capitalise,nameinlink]{cleveref}

\makeatletter
\renewcommand\appendix{\par
  \setcounter{chapter}{0}%
  \setcounter{section}{0}%
  \def\@chapapp{\appendixname}%
  \def\thechapter{\@Alph\c@chapter}}
  \makeatother

\begin{document}

TITLE

\tableofcontents

\chapter{Test Chapter 1}

Here is an idea (\cref{app:ch1}). The raw data is available in \cref{app:supp1}.

\chapter{Test Chapter 2}

Another idea.

{
\appendix
\chapter{Test Chapter 1}
\label{app:ch1}

\chapter{Test Chapter 2}
\label{app:ch2}
}

\crefalias{sectiom}{supp}

\renewcommand\chaptername{Supplementary}
\def\thechapter{S}

\chapter*{Supplementary material}
\section{Supplementary material of chapter 1}
\label{app:supp1}
\section{Supplementary material of chapter 2}
\label{app:supp2}


\end{document}

Using the appendices environment you can control things a little more finely:

Table of contents:

Text reference:

Supplementary material:

\documentclass{report}

\usepackage[toc,page,titletoc]{appendix}
\usepackage[capitalise,nameinlink]{cleveref}

\crefname{supp}{Supplement}{Supplements}

\begin{document}

\begin{center}
  TITLE
\end{center}

\tableofcontents

\chapter{Test Chapter 1}

Here is an idea (\cref{app:ch1}).
The raw data is available in \cref{app:supp1}.

\chapter{Test Chapter 2}

Another idea.

\begin{appendices}
\chapter{Test Chapter 1}
\label{app:ch1}

\chapter{Test Chapter 2}
\label{app:ch2}
\end{appendices}

\appendixpageoff
\appendixtitleoff
\renewcommand{\appendixtocname}{Supplementary material}
\begin{appendices}
  \setcounter{chapter}{19}
  \crefalias{section}{supp}
  \chapter*{Supplementary material}
  \section{Supplementary material of chapter 1}
  \label{app:supp1}
  \section{Supplementary material of chapter 2}
  \label{app:supp2}
\end{appendices}

\end{document}

The ingredients are as follows:

1. Ordinary appendices in their appendices environment with options controlled by the option passed to the appendix package
2. Supplementary material in a separate appendices environment, where the extra page and heading are turned off, the toc name is adjusted, the chapter counter is set to 19 (corresponding to "S"), the chapter title is provide by \chapter* and the section counter is aliased to supp
3. A \crefname instruction to print references to the supp counter with the name Supplement