pgfplots use full textwidth in subfigure environment

So I have two 3d plots I am drawing with pgfplots which I want to have on the same line, and I used the subfigure environment from the subcaption package for that (which I read was the preferred way to do it). The code is the following:

documentclass{article}
usepackage[utf8]{inputenc}

usepackage{subcaption}
usepackage{pgfplots} % plotting
usepackage{lipsum}

begin{document}

lipsum[1]
noindent
begin{figure}[h]
    centering
    % .475 as per https://tex.stackexchange.com/questions/241842/why-subfigure-doesnt-occupy-the-full-textwidth
    begin{subfigure}{.475textwidth}
        centering
    begin{tikzpicture}
        begin{axis}[
            unit vector ratio=1 1 1,
            view={-30}{30},
            xmin=0,
            xmax=1,
            xtick={0,1},
            xticklabels={(0,0), (1,0)},
            ymin=0,
            ymax=1,
            ytick={1},
            yticklabels={(0,1)},
            zmin=0,
            zmax=1,
            ztick={0,1},
            zticklabels={,,},
            width=textwidth
        ]
        
        addplot3[surf, domain=0:1, fill=white, faceted color=black] {min(x,y)};
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 0, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (0, x, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (1, x, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 1, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, x, {x});
      end{axis}
    end{tikzpicture}
    caption{tmin}
    end{subfigure}
    hfill
    begin{subfigure}{.475textwidth}
        centering
        begin{tikzpicture}
        begin{axis}[
            unit vector ratio=1 1 1,
            view={-30}{30},
            xmin=0,
            xmax=1,
            xtick={0,1},
            xticklabels={(0,0), (1,0)},
            ymin=0,
            ymax=1,
            ytick={1},
            yticklabels={(0,1)},
            zmin=0,
            zmax=1,
            ztick={0,1},
            zticklabels={,,},
            width=textwidth,
        ]

        addplot3[surf, domain=0:1, fill=white, faceted color=black] {0};
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 0, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (0, x, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (1, x, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 1, {x});
      end{axis}
    end{tikzpicture}
    caption{tL}
    end{subfigure}
end{figure}

noindent
lipsum[2-4]

end{document}

Now my problem is, that I expected the plots to be much bigger, since I set width=textwidth in axis, but the screenshot below shows that the plots are tiny.

What I tried so far: Setting scale only axis in the axis command (I admit I am not sure what that does), that indeed does make it bigger, but also not as big I’d hoped for and it seems to make it asymmetrical (see picture below).

(Notice that the green lines are of the same length!)

My guess is that there are some margins I am not aware of or I don’t understand what width=textwidth does.

Any help is greatly appreciated, I certainly cannot leave the plots like this.
cheers, alex

Edit as per suggestion in comments:
I added in draw[red] (current bounding box.south west) rectangle (current bounding box.north east); as suggested by @John Kormylo and the result looks as follows:

I also replaced hfill with hfil and ended the end{subfigure} line with a %, which made some minor difference, but in the picture with the bounding boxes it’s now obvious that lots of space left and right is still lost. Where is this space coming from and more importantly how can I get rid of it?

thanks again for the great tips so far! 🙂

documentclass{article}
usepackage[utf8]{inputenc}

usepackage{subcaption}
usepackage{pgfplots} % plotting
usepackage{lipsum}

makeatletter
newcounter{savewidthindex}
newsavebox{savewidthbox}
newcommand{newsavewidth}[2]% #1 = thesavewidthindex, #2 = estimated width needed
  {expandaftergdefcsname savewidth#1endcsname{#2}}
%
newenvironment{savewidth}{stepcounter{savewidthindex}%
  @ifundefined{savewidththesavewidthindex}{edefsavedwidth{thetextwidth}}%
    {edefsavedwidth{csname savewidththesavewidthindexendcsname}}%
  begin{lrbox}{savewidthbox}}%
 {end{lrbox}useboxsavewidthbox
  pgfmathsetlengthmacro{estimate}{textwidth/wdsavewidthbox*savedwidth}%
  immediatewrite@auxout{stringnewsavewidth{thesavewidthindex}{estimate}}}
makeatother

begin{document}

lipsum[1]
noindent
begin{figure}[h]
    centering
    % .475 as per https://tex.stackexchange.com/questions/241842/why-subfigure-doesnt-occupy-the-full-textwidth
    begin{subfigure}{.5textwidth}
        centering
    begin{savewidth}%
    begin{tikzpicture}
        begin{axis}[
            unit vector ratio=1 1 1,
            view={-30}{30},
            xmin=0,
            xmax=1,
            xtick={0,1},
            xticklabels={(0,0), (1,0)},
            ymin=0,
            ymax=1,
            ytick={1},
            yticklabels={(0,1)},
            zmin=0,
            zmax=1,
            ztick={0,1},
            zticklabels={,,},
            width=savedwidth
        ]
        
        addplot3[surf, domain=0:1, fill=white, faceted color=black] {min(x,y)};
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 0, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (0, x, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (1, x, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 1, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, x, {x});
      end{axis}
      draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}%
    end{savewidth}%
    caption{tmin}
    end{subfigure}%
    hfil
    begin{subfigure}{.5textwidth}
        centering
      begin{savewidth}%
        begin{tikzpicture}
        begin{axis}[
            unit vector ratio=1 1 1,
            view={-30}{30},
            xmin=0,
            xmax=1,
            xtick={0,1},
            xticklabels={(0,0), (1,0)},
            ymin=0,
            ymax=1,
            ytick={1},
            yticklabels={(0,1)},
            zmin=0,
            zmax=1,
            ztick={0,1},
            zticklabels={,,},
            width=savedwidth
        ]

        addplot3[surf, domain=0:1, fill=white, faceted color=black] {0};
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 0, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (0, x, 0);
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (1, x, {x});
        addplot3[domain=0:1, samples y=1, style={ultra thick}, black!70,smooth] (x, 1, {x});
      end{axis}
    draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}%
    end{savewidth}%
    caption{tL}
    end{subfigure}
end{figure}

noindent
lipsum[2-4]

end{document}