As organic matter (compost, mulch, etc.) is added to the garden, how do the beds not gradually grow higher? Does the organic matter decompose to literally nothing? Or do the particles just become so small that the beds’ height is relatively unaffected?

There are two actions at work. First is that the decomposition process continues after the compost has been added to the beds. A very small percentage of the matter, called humus, is left at the end of the decomposition process. As decades go by with more and more organic matter added to the beds, the soil level would increase.

The second action at work is that plants are being grown in the beds and they consume the humus along with the other elements that comprise the soil. If more organic matter is added to the beds than is consumed by the plants, then very slowly over time the beds will gradually grow higher.