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}{}
letORGeqfloateqfloat
defeqfloat{%
  letORIGINALcaptioncaption
  defcaption{%
    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}{}
letORGeqfloateqfloat
defeqfloat{%
  letORIGINALcaptioncaption
  defcaption{%
    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!