Doesn’t the biomass get dumped into the soil in a different place? You grow something, pick it, ship to a different country.

At a minimum, the roots are left in the soil.

Normally other parts of the crop are left in the field too, like leaves and stems and whatever else doesn't sell.

Not to forget that nowadays plants are optimized for high yield. I’d imagine the fruit/stem biomass ratio is becoming higher.

It needs to create biomass from something.

The main content of plant-created biomass comes from atmospheric CO2 and water, not from soil (well, roots extract water from the soil, but that's not what we mean by soil depletion). A significant minority is nitrogen, which either needs nitrogen-fixing plants (which extract it from atmosphere) or fertilization.

If the end-product is more carbon and nitrogen, doesn't that also mean it's less nutrient dense in other important micronutrients?

There is a long term trend that vegetables are getting less nutritious, yes. And it is speculated that it is because of soil depletion.

https://www.cookinglight.com/eating-smart/nutrition-101/frui...