You're right, barely visible. The solution increases the font size and makes the shaded text darker.
UPDATED II
(1) To include sections (formerly in white) and subsections, both with a larger font size.
(2) The vertical space between entries in the sidebar was reduced to allow more sections and subsections.
Also shaded (gray) sections and subsections have a smaller font size than the selected (colored).


\documentclass[dvipsnames]{beamer}
\usepackage{geometry,xcolor}
\geometry{paperwidth=148mm,paperheight=96mm}
\useoutertheme[width=20mm]{sidebar} %
%\usetheme{Berkeley}
\usecolortheme{beaver}
\addtobeamertemplate{navigation symbols}{}{%
\usebeamerfont{footline}%
\usebeamercolor[fg]{footline}%
\hspace{1em}%
\insertframenumber/\inserttotalframenumber
}
\setbeamercolor{footline}{fg=black}
\setbeamerfont{footline}{series=\small}
% From https://tex.stackexchange.com/a/137028/180429
%% ************************* added
\makeatletter
\setbeamertemplate{subsection in sidebar}
{%
\beamer@sidebarformat{5pt}{subsection in sidebar}{\color{darkred!80!gray}\footnotesize\insertsubsectionhead}% color and font size subsection << <<
}
\setbeamertemplate{subsection in sidebar shaded}
{%
\beamer@sidebarformat{5pt}{subsection in sidebar shaded}{\color{black!60}\scriptsize\insertsubsectionhead}% color and fontsize <<<
}
\setbeamertemplate{section in sidebar}% color and font size section << <<<
{%
\vbox{%
% \vskip1ex% <<<<
\beamer@sidebarformat{3pt}{section in sidebar}{\color{darkred!80!gray}\footnotesize\insertsectionhead}%
}%
}
\setbeamertemplate{section in sidebar shaded}% color and font size section << <<<
{%
\vbox{%
% \vskip1ex% <<<<
\beamer@sidebarformat{3pt}{section in sidebar shaded}{\color{black!60}\scriptsize\insertsectionhead}%
}%
}
\makeatother
%% *************************
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[babel]{csquotes}
\title[]{My presentation title}
\subtitle{Final Project}
\author[]{Euklid} % tricking LaTeX to think that the short title/author is the empty string as represented by []
\institute{Fancy University}
\date{2021}
\begin{document}
\frame{\titlepage}
\section{Background}
\begin{frame}{Background}{Natural numbers}
\begin{center}
[0,] 1, 2, 3, \dots{}
\end{center}
\end{frame}
\subsection{Introduction}
\begin{frame}{Introduction}{Motivation}
\begin{center}
The goal --- study math.
\end{center}
\end{frame}
\begin{frame}{Method}
The methods for this are...
\end{frame}
\section{Objective}
\begin{frame}{Objective}{Real numbers}
Rationals, Integers, Irrationals
\end{frame}
\subsection{Complex numbers?}
\begin{frame}{Next steps}{Complex numbers?}
Not yet.
\end{frame}
\subsection{What else?}
\begin{frame}{What else?}{What else?}
In the horizon.
\end{frame}
\subsection{A new grant}
\begin{frame}{A new grant}{It will be great!}
Everyone will appreciate it.
\end{frame}
\section{Main results so far}
\begin{frame}{Main results so far}{}
This is the most important part. \
\end{frame}
\section{Conclusions}
\begin{frame}{Conclusions}{To be done}
Not yet completed.
\end{frame}
\section{Thank you}
\begin{frame}{Thank you}{}
You all.
\end{frame}
\end{document}