This solution uses undocumented methods of obtaining the data tip lables (see inline comments). As with all undocumented approaches, things can change in future releases. When the user clicks on a stackedplot the datacursor values and the x value will appear in the command window along with the associated axis labels. You can easily print the value to a file instead. Note that callback functions do not return outputs.
See footnotes for important details.
% Create statckedplot
fig = figure();
x = linspace(-5*pi, 5*pi, 500)';
y = [sin(2*x), sin(x), sin(.5*x), sin(.2*x), -sin(.1*x)];
sph = stackedplot(y,'XData',x,'DisplayLabels',["A","B","C","D","E"]);
% Assign callback function when user clicks on figure
fig.WindowButtonDownFcn = {@myFunc, sph};
function myFunc(~,~,sph)
% sph is the stackedplot handle.
pause(0.5) % See footnote [1]
% Avoid seeing warning associated with undocumented methods
origState = warning('query', 'MATLAB:structOnObject');
cleanup = onCleanup(@()warning(origState));
warning('off','MATLAB:structOnObject')
S = struct(sph); % Undocumented
Sdc = struct(S.DataCursor); % Undocumented
% Get data tip values
dataTipLabels = Sdc.DatatipLabels;
dataTipStr = get([dataTipLabels{:}],'String');
axLabels = sph.DisplayLabels;
% If the vertical CursorLine is not visible (ie, the mouse is not in the axes) or
% if the data tips are all NaN (sometimes this happens on the first click only)
% then do nothing. Otherwise, print the data tip values and axis labels to command
% window.
if strcmpi(Sdc.CursorLine.Visible,'off') || all(cellfun('isempty',dataTipStr(1:end-1)))
return
else
yDataStr = compose(' %s = %.3g', string(axLabels), string(dataTipStr(1:end-1)));
fprintf('\nAt x = %s\n%s\n',dataTipStr{end},strjoin(yDataStr,newline))
end
end
%% Footnotes
% [1] The pause(0.5) is needed to give time for the data tip values to
% update. Notice that the line must remain still for a brief period
% before the datatips appear. In that time, the datatip values from
% the previous datatip appearance are stored and we must wait for them
% to regenerate before returning the updated value. This lag is a
% property of the stackedplot data cursor: Sdc.LingerTime.
