Usually, there's a menu that tells you what's on the various pizzas. Isn't that your experience? I am saying, in a puzzled way, why do you have to ask?
These days, almost every sort of eating place describes in great (and often ridiculous) detail exactly what each dish is composed of. So, I must say that I find your question unreal, not based on the reality of buying pizzas as I know it, (or anything else) in the UK and the USA.
On the other hand, many people in the UK and the USA want to assure themselves very precisely about all the ingredients of everything they eat 'out', because they have allergies, dietary preferences or ingredients they disapprove of either for health or geo- political reasons.
If you really need to ask about pizza toppings, you can certainly enquire like this: What are the toppings on the pizza primavera? Some people might think it's an odd question (and who cares what 'people' think), but that really is an OK question if you really need to know what's on this type of pizza; it's grammatically correct too.
The generic, all-embracing question about the ingredients of anything would be "What's in the [name of dish]?"
My personal question to a pizza parlour would be "Whatexactly is in the pizza dough?" That's because there are various ingredients possible in a non-authentic pizza dough, that I am unwilling to consume for one reason or another. For instance, I refuse to eat anything with palm oil in it, or to consume hydrogenated trans- fatty acids.
I suggest that "What's in the ..." is a good generic way of asking about ingredients in any dish, or components of a dish.
I would then seek detailed assurance about whatever was of particular concern to me, asking, for example, 'Is there any nut product in this dish?', 'Is there any palm-oil in this dish?', ' Are there any animal products in this dish?', 'Do you use MSG?', 'Is this halal/kosher?', 'Are there any GM ingredients in this?'
Of course, if I had any allergies I would ask if there was that allergenic product in the recipe.
Many years ago, a friend of mine in Paris, France nearly died because a chef had casually chucked some left-over fish stock into the chicken soup my friend had ordered. These days, savvy customers take nothing for granted and, usually, food establishments are much more aware of their responsibilities. They do not want to be sued or face criminal prosecution and they write warnings on the menus, just as manufacturers put warnings on their products.
There are occasions where a menu is not accessible such as ordering on the phone, or when you have friends visiting and you suggest getting a pizza for dinner and one of them says, Why don't we get a large quattro staggioni?. If you're not familiar with, it you might say, What's on it?
Gabriel, your question sounds very normal and correct to me. If you mention one of the pizzas on the list and ask "What's on it?" they will assume you mean the toppings, not all the ingredients.
If you want to know about the cheese, tomato sauce or dough, ask separately. Or ask "what's in it?"
Many menus list only names and prices. Even ones that list toppings usually "forget" some of them.
And the exact toppings is different in every pizza place. A "mushrooms only" pizza may be the same everywhere (it isn't, by the way) but the "special", the "italian", the "meat lovers", the "everything" and a dozen other pizzas are different at two shops a block apart.
If you sit down to eat in a "fancy" place, you cannot even assume it has tomato sauce and cheese on top. At least not in Boston or California. It's safer to ask. < Topic drift removed. Cagey, moderator. >