! Extra }, or forgotten endgroup.
pgf@externalend ->unskip egroup egroup
                                           {def pgf@external@trim {0}def ...
l.88   end{forest}

documentclass[a4paper,12pt, twoside,dvipsnames]{article}

usepackage[dvipsnames]{xcolor}

usepackage{tikz}
usetikzlibrary{external}
tikzexternalize[mode=list and make, prefix=ext-tikz/]
usepackage[external]{forest}

usetikzlibrary{fadings, arrows.meta}


makeatletter
newififtikz@shading@path

tikzset{
    % There are three circumstances in which the fading sep is needed:
    % 1. Arrows which do not update the bounding box (which is most of them).
    % 2. Line caps/joins and mitres that extend outside the natural bounding
    %    box of the path (these are not calculated by PGF).
    % 3. Other reasons that haven't been anticipated.
    fading xsep/.store in=pgfpathfadingxsep,
    fading ysep/.store in=pgfpathfadingysep,
    fading sep/.style={fading xsep=#1, fading ysep=#1},
    fading sep=0.0cm,
    shading path/.code={%
        % Prevent this stuff happning recursively.
        iftikz@shading@path%
        else%
            tikz@shading@pathtrue%
            % tikz@addmode installs the `modes' (e.g., fill, draw, shade)
            % to be applied to the path. It isn't usualy for doing more
            % changes to the path's construction.
            tikz@addmode{%
                pgfgetpathpgf@currentfadingpath%
                % Get the boudning box of the current path size including the fading sep
                pgfextract@processpgf@fadingpath@southwest{pgfpointadd{pgfqpoint{pgf@pathminx}{pgf@pathminy}}%
                    {pgfpoint{-pgfpathfadingxsep}{-pgfpathfadingysep}}}%%
                pgfextract@processpgf@fadingpath@northeast{pgfpointadd{pgfqpoint{pgf@pathmaxx}{pgf@pathmaxy}}%
                    {pgfpoint{pgfpathfadingxsep}{pgfpathfadingysep}}}%
                % Clear the path
                pgfsetpathpgfutil@empty%
                % Interrupt the path and picture to create a fading.
                pgfinterruptpath%
                pgfinterruptpicture%
                    begin{tikzfadingfrompicture}[name=.]
                        path [shade=none,fill=none, #1] pgfextra{%
                            % Set the softpath. Any transformations in #1 will have no effect.
                            % This will *not* update the bounding box...
                            pgfsetpathpgf@currentfadingpath%
                            % ...so it is done manually.
                            pgf@fadingpath@southwest
                            expandafterpgf@protocolsizes{thepgf@x}{thepgf@y}%
                            pgf@fadingpath@northeast%
                            expandafterpgf@protocolsizes{thepgf@x}{thepgf@y}%
                        };
                        % Now get the bounding of the picture.
                        xdefpgf@fadingboundingbox@southwest{noexpandpgfqpoint{thepgf@picminx}{thepgf@picminy}}%
                        xdefpgf@fadingboundingbox@northeast{noexpandpgfqpoint{thepgf@picmaxx}{thepgf@picmaxy}}%
                        %
                    end{tikzfadingfrompicture}%
                endpgfinterruptpicture%
                endpgfinterruptpath%
                % Install a rectangle that covers the shaded/faded path picture.
                pgfpathrectanglecorners{pgf@fadingboundingbox@southwest}{pgf@fadingboundingbox@northeast}%
                % Make the fading happen.
                deftikz@path@fading{.}%
                tikz@mode@fade@pathtrue%
                tikz@fade@adjustfalse%10pt
                % Shift the fading to the mid point of the rectangle
                pgfpointscale{0.5}{pgfpointadd{pgf@fadingboundingbox@southwest}{pgf@fadingboundingbox@northeast}}%
                edeftikz@fade@transform{shift={(thepgf@x,thepgf@y)}}%
            }%
        fi%
    }
}

begin{document}

begingroup
    centering
    begin{forest}
        [, phantom, for children={fit=band}, s sep'+=60pt
            [ 2, name=l1 ]
            [ 2, name=r1 ]
        ]
        path [left color=orange, right color=MidnightBlue, shading path={draw=transparent!0, dashed, -Latex}] (l1) .. controls ++(0,-1) and ++(0,-1) .. (r1);
    end{forest}
endgroup

end{document}