algorithm2e with booktabs style and listing the algorithms in toc

I’m using the solution that @egreg provided on this answer, but I’m using the algorithm2e package instead of algorithms.

I’d like to retain the design from booktabs but the command listofalgorithms prints an empty list.

I think this is due to the fact that now the algorithms are figures, so the .loa file results to be empty.
I don’t know how to proceed, any suggestion is appreciated.

This is my not working MWE

documentclass{book}

usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}

usepackage{algorithm2e}
usepackage{booktabs}

# https://tex.stackexchange.com/a/345745/127473
makeatletter
newcommandfs@booktabsruled{%
  def@fs@cfont{bfseriesstrut}let@fs@captfloatc@ruled
  def@fs@pre{hrule heightheavyrulewidth depth0pt kernbelowrulesep}%
  def@fs@mid{kernaboverulesephrule heightlightrulewidthkernbelowrulesep}%
  def@fs@post{kernaboverulesephrule heightheavyrulewidthrelax}%
  let@fs@iftopcaptiftrue
}
makeatother

usepackage{float}
newfloat{algorithm}{h}{alg}

floatstyle{booktabsruled}
restylefloat{algorithm}

begin{document}

listofalgorithms % empty

begin{algorithm} 
    caption{test}
end{algorithm}

end{document}

And this is the result

documentclass{article}

usepackage[ruled]{algorithm2e}
usepackage{booktabs}

% Values shamelessly taken from egreg's answer in 
% https://tex.stackexchange.com/a/345745/82917
makeatletter
renewcommand*{@algocf@pre@ruled}{hrule heightheavyrulewidth depth0pt kernbelowrulesep}
renewcommand*{algocf@caption@ruled}{boxalgocf@capboxkernaboverulesephrule heightlightrulewidthkernbelowrulesep}
renewcommand*{@algocf@post@ruled}{kernaboverulesephrule heightheavyrulewidthrelax}
makeatother

begin{document}

listofalgorithms

begin{algorithm} 
 While{condition}{
  something;
 }
caption{Some nice algorithm}
end{algorithm}

end{document}