The bag of coffee I am using instructs to "Add 2 1/2 tablespoons (37 ml)" of ground coffee. When I measure out 2 1/2 tablespoons onto my food scale, it only comes out to about 13 ml.
Why does my 2 1/2 tablespoon measurement not equal 37 ml?
Your scale is measuring weight, not volume.
Some scales do have an option to "convert" to volume, but they have to do so based on density; they don't actually know what's on top of them. So unless yours is really fancy, and has a bunch of densities programmed into it, so that you can say "this is flour" and let it convert, it's probably just assuming everything is water, with a density of 1g/mL.
And this should be really easy to confirm. Just toggle it from weight to volume. If it says 13mL is 13g, then that's what it's doing.
So then it's telling you that your 2.5 tablespoons of coffee is 13g, not 13mL, because it's around 1/3 as dense as water.