Réduire la taille d'un symbole

\documentclass{article}
\usepackage{amsmath}
\usepackage{etoolbox}

\makeatletter
% Commande d'egreg (https://tex.stackexchange.com/a/499972/73317)
\newcommand*{\math@param}[3]{%
  \fontdimen#3
  \ifx#1\displaystyle\textfont#2
  \else\ifx#1\textstyle\textfont#2
  \else\ifx#1\scriptstyle\scriptfont#2
  \else\scriptscriptfont#2 \fi\fi\fi
}

\newcommand*{\my@smaller@style}[1]{%
  \ifx#1\displaystyle\scriptstyle
  \else\ifx#1\textstyle\scriptstyle
  \else\scriptscriptstyle \fi\fi
}

\newcommand*{\makeSmaller}[3]{%
  \let#2#1%
  \newcommand*{#3}{%
    \mathrel{\expandafter\mathpalette
             \csname my@\expandafter\@gobble\string#3\endcsname
             \relax}%
  }%
  %
  \csdef{my@\expandafter\@gobble\string#3}##1##2{%
    \begingroup
      \edef\my@smaller{\my@smaller@style{##1}}%
      \raisebox{\dimexpr \math@param{##1}{2}{22} -
                \expandafter\math@param\expandafter{\my@smaller}{2}{22}}{%
        $\m@th\my@smaller@style{##1} #2$}%
    \endgroup
  }%
}

\makeSmaller{\odot}{\odotORIG}{\smallodot}
\makeSmaller{\oplus}{\oplusORIG}{\smalloplus}
\makeatother

\begin{document}

\[ (2\odot x)\oplus (2\odot y)\oplus (3\odot x\odot y)\oplus x^{\odot 2} \]
\let\odot\smallodot
\let\oplus\smalloplus
\vspace*{-1.5\baselineskip}%
\[ (2\odot x)\oplus (2\odot y)\oplus (3\odot x\odot y)\oplus x^{\odot 2} \]

\end{document}