Can not restrict the table
\documentclass[pdflatex, sn-aps]{sn-jnl}% American Physical Society (APS) Reference Style
%%%% Standard Packages
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{comment}
\usepackage[center]{caption}
\usepackage{subcaption}
\usepackage{float}
\usepackage[misc]{ifsym}
\usepackage{csquotes}
\usepackage[section]{placeins}
\usepackage{siunitx}
%%<additional latex packages if required can be included here>
\usepackage{amsmath}
\usepackage{graphicx}
\graphicspath{{./images/}}
%Table packages
\usepackage[figuresright]{rotating}
\setlength{\rotFPtop}{0pt plus 1fil}
\usepackage{booktabs, makecell, multirow, tabularx}
\renewcommand{\theadfont}{\footnotesize\bfseries}
\renewcommand\theadgape{}
\newcolumntype{L}{>{\raggedright\arraybackslash}X}
\newcolumntype{P}[1]{>{\raggedright\arraybackslash}p{#1}}
\raggedbottom
%%\unnumbered% uncomment this for unnumbered level heads
\begin{document}
\begin{table}
\centering
% table caption is above the table
\caption{Part of the patient data collected via the questionnaire}
\label{tab:Patient data} % Give a unique label
% For LaTeX tables use
\begin{tabular} { c
c
c
c
c
c
c
c
c
}
\toprule
\thead{Patient\Number} &\thead{$T_{before}$\(week1)} & \thead{$T_{after}$\(week1)}& \thead{$C_{week1}$}
& \thead{$C_{week2}$}& \thead{$C_{week3}$}& \thead{$C_{week4}$}& \thead{Overall\improvement}&\thead{$T_{after}$\(week4)}\
\midrule\
1&41&34&17.07&17.26&20.62&23.67&6.60&32 \
\addlinespace
2&41&41&0.00&3.49&6.47&7.16&7.16&35 \
\addlinespace
3&41&34&17.07&18.88&19.87&21.12&4.05&30 \
\addlinespace
4&89&88&1.12&3.27&6.13&8.30&7.18&81 \
\addlinespace
12&50&50&0.00&0.00&0.00&0.00&0.00&50 \
\bottomrule
\end{tabular}
\end{table}
\end{document}


\footnotesizebefore the\begin{tabular}so it is smaller. – David Carlisle Jan 26 '22 at 09:50tabulartotabular*and add "forced" width, with flexible spaces between columns (see this page), as an example the definition could be:\begin{tabular*}{\linewidth}{c @{\extracolsep{\fill}} c c c c c c c c} ... \end{tabular*}. But your table will be too narrow and probably will not look well. – Celdor Jan 26 '22 at 10:13\setlength{\tabcolsep}{0pt}before thetabular/tabular*environment. BTW adding\footnotesizeas David mentioned sets smaller font inside a table and it should work. – Celdor Jan 26 '22 at 11:47