How to remove bibliography from progress on Beamer?

Question

I created a Beamer presentation that has 15 frames of content and 5 frames of references. I also enabled the progress bar, which indicates how far along I am through my presentation. However, the progress is calculated based on the total 20 frames of my presentation. Thus, when I'm on my last slide, it says that I'm only 3/4 into the presentation.

Is there a way to indicate which is the last slide of content, so that no frames beyond the point are counted toward my progress? I would rather not use the \appendix command for two reasons: (1) I already have appendix slides included in my presentation, and (2) I would like for the page count to continue unchanged throughout the bibliography. I've looked for an answer online, but I haven't come across anything that addresses my concern.

FYI, I'm using the biblatex package for my bibliography and the command \printbibliography.

MWE below:

\documentclass{beamer}
\usetheme{metropolis}
%make progress-bar thicker
\makeatletter
\setlength{\metropolis@progressonsectionpage@linewidth}{2.5pt}
\makeatother
\title{My title}
\author{Me}
\usepackage{lipsum}
% Set bibliography
\usepackage[style=authoryear]{biblatex}
\addbibresource{ref.bib}
\usepackage{filecontents}
% Add references
\begin{filecontents}{ref.bib}
    @book{key1,
        author = {Author, A.},
        year = {2001},
        title = {Title1},
        publisher = {Publisher},
    }
    @book{key2,
        author = {Author, B.},
        year = {2002},
        title = {Title2},
        publisher = {Publisher},
    }
\end{filecontents}
\begin{document}
\maketitle


\section{First concept}
\begin{frame}{First frame}
    \lipsum[1]
\end{frame}


\section{First citation}
\begin{frame}
    \frametitle{First citation}
    ``First quote.'' \cite{key1}
\end{frame}


\section{Last citation}
\begin{frame}{Last frame}
    ``Second quote.'' \cite{key2}
\end{frame}


\begin{frame}[t]{References}
    \printbibliography[heading=none]
\end{frame}


\end{document}

Result of this code is shown below:

In general, I'd like for the progress-bar under 'First Concept' to be at zero, since we are about to get to the 'first frame'; I want the progress-bar under 'First citation' at 1/3 because 'First citation' is my second frame; and the progress-bar under 'Last citation' should be at 2/3, since 'Last frame' is the last content frame.

Nonetheless, the last section has a progress-bar at 1/2 because it's counting 'References' as a content frame and it takes up one quarter of my presentation.

@moewe, here's the error I receive

Answer 1

You may want to try the following, which remembers the frame number of the bibliography and uses that (minus 1) instead of the total frame number to calculate the progress bar.

\documentclass{beamer}
\usetheme{metropolis}
\title{My title}
\author{Me}
\usepackage{lipsum}
\usepackage[style=authoryear]{biblatex}
\addbibresource{biblatex-examples.bib}
\makeatletter
\setlength{\metropolis@progressonsectionpage@linewidth}{2.5pt}
\newcommand\beamer@startframeofbib{2}
\newcommand\beamer@bibframes[1]{\gdef\beamer@startframeofbib{#1}}
\defbibheading{pagenumber}[\refname]{%
  \addtocontents{nav}{\protect\headcommand{\protect\beamer@bibframes{\the\c@framenumber}}}}
\setbeamertemplate{progress bar in section page}{%
  \setlength{\metropolis@progressonsectionpage}{%
    \textwidth * \ratio{\insertframenumber pt}{\the\numexpr\beamer@startframeofbib-1\relax pt}%
  }%
  \begin{tikzpicture}
    \fill[bg] (0,0) rectangle (\textwidth, \metropolis@progressonsectionpage@linewidth);
    \fill[fg] (0,0) rectangle (\metropolis@progressonsectionpage, \metropolis@progressonsectionpage@linewidth);
  \end{tikzpicture}%
}
\makeatother
\begin{document}
\maketitle


\section{First concept}
\begin{frame}{First frame}
    \lipsum[1]
\end{frame}


\section{First citation}
\begin{frame}
    \frametitle{First citation}
    ``First quote.'' \cite{sigfridsson}
\end{frame}


\section{Last citation}
\begin{frame}{Last frame}
    ``Second quote.'' \cite{nussbaum}
\end{frame}

\appendix
\begin{frame}[t]{References}
    \printbibliography[heading=pagenumber]
\end{frame}


\end{document}