Plots: retrieve axes width in final figure, and other object dimensions?

It would be useful to be able to retrieve the exact dimensions (in pixels, or other consistent units) of the elements of a plot. For instance, if one does:

plt = scatter(rand(10),size=(500,500))
display(plt) # or savefig

How can I get the exact length of the axes in the final figure? Specifically, the complete figure has 500x500 pixels, and the axes only span part of that width. In particular, the width of the axes are dependent on the presence of a title in the figure, of legends, etc, ticks, etc.

Related to that, if we use markersize=50 or something else in this plot, we can set the marker size, but it is not clear at all how that size is related to the size of the figure or, more importantly, with the limits of the axes. If we could also retrieve the axes widths and marker width in the same units, the marker size could be used for quantitative representation of objects of different dimensions in a practical way.

This is a followup of this question, for which I provided a very ugly workaround that depends on opening the figure in Inkscape to actually measure the dimensions generated in a specific plot context: How to plot circles with given radii using Plots