Would I find it gross? Would I chip a tooth trying to eat it? Was it even made from the same species of plant?
There was no single “Mesopotamian bread”. Their history covers thousands of years, they used different grains for bread making, different styles of ovens, different ingredients, they had both leavened and unleavened breads, flatbreads and loaves and pastry crusts, plenty of other variations. There are four thousand year old Mesopotamian clay tablets listing hundreds of ingredients and different types of dishes. They list around 300 types of breads.
Taking a general approach to your question, the popular grains at the time were barley, wheat and rye. All were used to make breads. Grains were also used to make beer and different styles of gruel or pottage. Narrowing it down to wheat, the kind they used was emmer or Triticum turgidarum, an ancient variety of wheat. You can still buy it today from specialty food stores and try it yourself to see what it tastes like. It has slightly less gluten than modern bread flour, so it doesn’t rise quite as well. It has a nuttier taste, the flour is stickier and hard to handle. But it’ll still produce a very modern-looking loaf of bread.
In the very early days they used “open” ovens, which were basically hollow clay cylinders, open at both ends. You place a cylinder vertically, build a fire inside at the lower end, wait for it to heat up the cylinder, then you stick the bread on the outer walls of the cylinder to bake it. If this reminds you of the Indian tandoor, it’s probably not an accident, the Mesopotamian word for this oven was “tannur”. Around the 3rd millennium BC, we also see covered dome-type ovens, so they could produce loaves of bread as well as flatbreads. Leavening also dates to at least this period, if not earlier.
The flour was stone ground, as it has been throughout history until very recently when metal grinding wheels came into widespread use during the industrial revolution. The flour was sifted after grinding, so no, you wouldn’t chip any teeth from eating it unless someone was lazy with the sifting. However, sifting can’t remove very fine stone dust, so if you ate it every day for your lifetime, your tooth enamel would probably wear out as we see in the teeth of Egyptian mummies. They didn’t grind the flour as fine as we do today, so less of the bran was removed. This would make it more like whole wheat flour today rather than refined flour.
There were literally hundreds of recipes for bread. One of the better known collections is from Jean Bottero’s translation of a collection of clay tablets from around 1,900 – 1,700 BC, which list a lot of recipes from their cuisine, including around a hundred types of soup, a couple of dozen cheeses, dozens of meat stews, pies, etc. The recipes don’t go into much detail, so you can’t really make them in a modern kitchen without introducing guesswork. But we know they weren’t just baking breads, they were making pastry crusts for pies stuffed with meat and fowl inside, they were cooking them by baking, steaming and boiling. They used milk and yogurt in their doughs along with water, they tended to flavor breads with different kinds of stuff including onions, garlic, leeks and spices. Surprisingly, they didn’t use a lot of salt as seasoning.
So in summary, no it wouldn’t have tasted “gross”. The quality would have varied tremendously depending on whether you were eating in a peasant’s home or dining at the palace, what kind of bread you were eating. But pretty much all the “innovations” we use in modern baking had already been invented at the time.
If you’re interested, this is Bottero’s paper on the tablets I mentioned earlier: