On a private vanilla 1.14 server hosted by Shockbyte, I can give a farmer 15 potatoes, and it will level up by one, however, I can also give it, say, 45 potatoes, and the villager will still only level up the one bar. This makes it so trading has to be done 15 potatoes at a time to level the villager up, instead of shift-clicking the trade and leveling it up as many times as there were trades.

I was expecting the villager to level up one bar per every 15 potatoes, coal, etc.

What actually happened was, I gave it a stack of potatoes (etc.) in that trade slot, and it leveled up by one.