Placing equation's caption on outermargin with LaTex

Question

I am using LaTex (pdflatex) to write my thesis. I am using a two-sides book documentclass.
I want to create a layout with a big outermargin where to write the captions of figures, tables and equations.

I found that the sidecap package works perfectly for figures and tables with these settings:

\usepackage[margincaption,outercaption,ragged,wide]{sidecap}

\sidecaptionvpos{figure}{t} 
\sidecaptionvpos{table}{t}

% Custom commands for captions
\captionsetup[SCfigure]{
    format=plain,
    font=footnotesize,
    labelfont=bf,
}
\captionsetup[SCtable]{
    format=plain,
    font=footnotesize,
    labelfont=bf,
}

At the same time I used the eqfloat declaration to be able to write the caption for equations:

\usepackage{aliascnt}
\newaliascnt{eqfloat}{equation}
\newfloat{eqfloat}{h}{eqflts}
\floatname{eqfloat}{Equation}

\newcommand*{\ORGeqfloat}{}
\let\ORGeqfloat\eqfloat
\def\eqfloat{%
  \let\ORIGINALcaption\caption
  \def\caption{%
    \addtocounter{equation}{-1}%
    \ORIGINALcaption
  }%
  \ORGeqfloat
}

\captionsetup[eqfloat]{
    format=plain, % Plain format
    font=footnotesize, % Footnotesize font size
    labelfont=bf, % Bold label (title)
}

This is the appearance of the pdf now, I would like to also have the equation's caption on the side

Here an example code to test it:

\documentclass[a4paper, twoside]{book}
\usepackage{titlesec} % Customize section titles
\usepackage[T1]{fontenc} % Ensure correct font encoding
\usepackage[english]{babel} % English rules handling
\usepackage[utf8]{inputenc} % UTF-8 input encoding
\usepackage{graphicx} % include figures
\usepackage{tabularx} % Creates adjustable-width columns tables
\usepackage{lipsum} % Lorem ipsum text for testing
\usepackage{booktabs} % New rules for table formatting
\usepackage{caption} % Customizes captions for figures and tables
\usepackage{float}
\usepackage{aliascnt}


% Set up page layout with wider outer 
\usepackage{geometry}
\geometry{
  inner=2.5cm,
  outer=5cm,
  top=3cm,
  bottom=3cm,
  marginparsep=0.5cm,
  marginparwidth=4cm,
}
\usepackage[margincaption,outercaption,ragged,wide]{sidecap}

\sidecaptionvpos{figure}{b} 
\sidecaptionvpos{table}{b}

% Custom commands for captions
\captionsetup[SCfigure]{
    format=plain,
    font=footnotesize,
    labelfont=bf,
}
\captionsetup[SCtable]{
    format=plain,
    font=footnotesize,
    labelfont=bf,
}


\newaliascnt{eqfloat}{equation}
\newfloat{eqfloat}{h}{eqflts}
\floatname{eqfloat}{Equation}

\newcommand*{\ORGeqfloat}{}
\let\ORGeqfloat\eqfloat
\def\eqfloat{%
  \let\ORIGINALcaption\caption
  \def\caption{%
    \addtocounter{equation}{-1}%
    \ORIGINALcaption
  }%
  \ORGeqfloat
}

\captionsetup[eqfloat]{
    format=plain, % Plain format
    font=footnotesize, % Footnotesize font size
    labelfont=bf, % Bold label (title)
}



\begin{document}

\lipsum[1]

\begin{SCtable}[h]
    \centering
    \begin{tabular}{ll}
      \toprule
      Name & Age \\
      \midrule
      Alice & 25 \\
      Bob & 30 \\
      \bottomrule
    \end{tabular}
    \caption{A sample table}
  \end{SCtable}
\lipsum[2]

\begin{eqfloat}
  \caption{The famous equation by Einstein}
    \begin{equation}
      E = mc^2
    \end{equation}
\end{eqfloat}
  

\lipsum[4]

\begin{SCfigure}[h]
        \includegraphics[width=5cm]{example-image}
        \caption{Caption for your figure}
\end{SCfigure}
\lipsum[3]
    
\end{document}

I tried to redeclare the caption for the eqfloat in the text by using the marginnote package, but something fails.

I also tried to use the minipage package, but I have not clear how to properly use it with the eqfloat environment.

Anyone can help me? I need any solution that do not require to specifically change everything when i want to comment an equation, since there will be many!

Thanks in advance!