First of all I would remove packages tocbibind
and tocstyle
and the \addcontentsline
statements from your MWE:
\documentclass[
twoside=false,
listof=totoc,% add a tocentry for lists like LOF and LOT
toc=chapterentrywithdots% dots as line filler for chapter entries in TOC
]{scrbook}
\setuptoc{toc}{totoc}% add a tocentry for TOC
\DeclareTOCStyleEntry[
dynnumwidth,% adjust the space for part numbers in TOC as needed
entrynumberformat=\partnumberwithprefix,% part number with prefix
pagenumberformat=\gobble% remove page number of part entries in TOC
]{tocline}{part}
\newcommand\partnumberwithprefix[1]{\partname\nobreakspace#1}
\newcommand\gobble[1]{}
\addtokomafont{chapterentrypagenumber}{\mdseries}
\begin{document}
\frontmatter
\addpart{Front Matter}
\tableofcontents
\listoftables
\listoffigures
\mainmatter
\addpart{Report}
\chapter{Chapter 1}
\section{Section 1}
\section{Section 2}
\section{Section 3}
\appendix
\addpart{Appendices}
\chapter{Appendix 1}
\section{Appendix Section 1}
\section{Appendix Section 2}
\section{Appendix Section 3}
\end{document}
Result:

If TOC, LOF and LOT should be sections instead chapters you could use lists=leveldown
and \setuptoc{toc}{leveldown}
:
\documentclass[
twoside=false,
listof=totoc,
listof=leveldown,% <- added
toc=chapterentrywithdots
]{scrbook}
\setuptoc{toc}{totoc,leveldown}% <- changed
\DeclareTOCStyleEntry[
dynnumwidth,
entrynumberformat=\partnumberwithprefix,
pagenumberformat=\gobble
]{tocline}{part}
\newcommand\partnumberwithprefix[1]{\partname\nobreakspace#1}
\newcommand\gobble[1]{}
\addtokomafont{chapterentrypagenumber}{\mdseries}
\begin{document}
\frontmatter
\addpart{Front Matter}
\tableofcontents
\listoftables
\listoffigures
\mainmatter
\addpart{Report}
\chapter{Chapter 1}
\section{Section 1}
\section{Section 2}
\section{Section 3}
\appendix
\addpart{Appendices}
\chapter{Appendix 1}
\section{Appendix Section 1}
\section{Appendix Section 2}
\section{Appendix Section 3}
\end{document}
Result:

But if you really want that TOC, LOF and LOT are still chapters but get TOC entries like sections, then you could add
\BeforeTOCHead{%
\renewcommand\addchaptertocentry[2]
{\addtocentrydefault{section}{#1}{#2}}%
}
to the first example.

Code:
\documentclass[
twoside=false,
listof=totoc,
toc=chapterentrywithdots
]{scrbook}
\setuptoc{toc}{totoc}
\BeforeTOCHead{%
\renewcommand\addchaptertocentry[2]
{\addtocentrydefault{section}{#1}{#2}}%
}
\DeclareTOCStyleEntry[
dynnumwidth,
entrynumberformat=\partnumberwithprefix,
pagenumberformat=\gobble
]{tocline}{part}
\newcommand\partnumberwithprefix[1]{\partname\nobreakspace#1}
\newcommand\gobble[1]{}
\addtokomafont{chapterentrypagenumber}{\mdseries}
\begin{document}
\frontmatter
\addpart{Front Matter}
\tableofcontents
\listoftables
\listoffigures
\mainmatter
\addpart{Report}
\chapter{Chapter 1}
\section{Section 1}
\section{Section 2}
\section{Section 3}
\appendix
\addpart{Appendices}
\chapter{Appendix 1}
\section{Appendix Section 1}
\section{Appendix Section 2}
\section{Appendix Section 3}
\end{document}
tocbibind
and KOMA? ... and explicit\addcontentsline
statements..