As I don't want my sections ... paragraphs to stay unnumbered, I wrote \setcounter{tocdepth}{5} \setcounter{secnumdepth}{0}. With cleveref I cannot refer to unnumbered sections as "section" at all.
To be more clear: I defined a new ref-format \RenewDocumentCommand\fullref{m}{\namecref{#1} \nameref{#1} \vpageref{#1}}, which should give something like "section sectiontitle on page 2" or "subsection sectiontitle on page 4.
% uses-*- MODE: latex; TeX-engine: luatex; coding: utf-8; -*-
\documentclass{scrartcl}
\usepackage[main=ngerman]{babel}
\usepackage[german,final]{varioref}
\usepackage{hyperref}
\usepackage[german,nameinlink]{cleveref}
\makeatletter
\RenewDocumentCommand\fullref{m}{\namecref{#1} \nameref{#1}
\vpageref{#1}}
\setcounter{tocdepth}{5}
\setcounter{secnumdepth}{0} % <---
\makeatother
\begin{document}
\section{I'm Section}
\label{sec:section}
bla
see \namecref{sec:subsubsection}
see \fullref{sec:subsubsection}
\newpage
\subsection{I'm Subsection}
\label{sec:subsection}
bla
bla
see \namecref{sec:section}
see \fullref{sec:section}
see \namecref{sec:subsection}
see \fullref{sec:subsection}
\newpage
\subsubsection{I'm Child of Subsection}
\label{sec:subsubsection}
\end{document}

\labelonly stores 4 values in the aux file:\@currentlabel,\thepage,\@currentlabelnameand\@currentHref. The section title is stored in\@currentlabelnamewhich is a missuse of the entry IMHO. – John Kormylo Jul 31 '23 at 23:14\currentHref. This doesn't always work (see https://tex.stackexchange.com/questions/643473/unexpected-table-figure-reference/643489?r=SearchResults&s=3%7C10.6660#643489). – John Kormylo Aug 01 '23 at 13:01