Conflict with natbib

[mjthoraval]

When I use jabbrv with natbib, it breaks the commands \citet and \citeauthor.

Here is a minimal example:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

%Import the natbib package and sets a bibliography  and citation styles
%\usepackage[numbers, sort&compress]{natbib}
\usepackage{natbib}
\usepackage{jabbrv} % Use a custom jabbrv-compatible style (.bst file) in \bibliographystyle
% Use a custom jabbrv-compatible style (.bst file) in \bibliographystyle when using the package jabbrv
\bibliographystyle{unsrtnat}
%\bibliographystyle{jabbrv_unsrtnat} % Does not seem to be compatible with jabbrv

% Write the bibtex file
% https://latexref.xyz/fr/filecontents.html
\begin{filecontents*}[overwrite]{References.bib}
@article{einstein,
  author =       "Albert Einstein",
  title =        "Test title",
  journal =      "Annalen der Physik",
  volume =       "322",
  number =       "10",
  pages =        "891--921",
  year =         "1905",
  DOI =          "10.1002/andp.19053221004"
}
\end{filecontents*}

\title{Test Natbib and Jabbrv}
\author{}
\date{}

\begin{document}
\maketitle

Test of the different Natbib commands:
\begin{enumerate}
    \item \verb|cite|: \cite{einstein}
    \item \verb|citet|: \citet{einstein}
    \item \verb|citep|: \citep{einstein}
    \item \citeauthor{einstein}
\end{enumerate}


\bibliography{References}

\end{document}

If I remove the jabbrv package, here is the expected result:

After adding the jabbrv package, here is the result:

I get the following error:
! Package natbib Error: Bibliography not compatible with author-year citations.
And warnings:
Package natbib Warning: Author undefined for citation`einstein'

Any idea of what is going wrong and how it could be fixed?
Thank you.