Why do restaurants and cafes in Ukraine make a transaction on each food separately?

The businesses have incentives to split checks because they are used to aggressive expense optimization. In Ukraine this has been an edge case, which outside viewer sees as inability of government to collect taxes properly.

So it is about taxes (it is a rule of thumb to follow the money, so it is about cutting seller expenses anyway), but not in the way described in the earlier answer (annual limit for income per low taxation entity is above $50,000 and the threshold is high enough to not abuse customers by bill splitting per plate!).

The article I linked in comment earlier explains (in Russian) details how businesses are cheating in their sales and provision of services. One of the cases is check splitting in particular.

… Almost always you are charged twice in a restaurant of a cafe. You get one bill for the bar beverages, and the other for the snacks. The first receipt has a name of certain LLC on it, as alcohol seller license is expensive and can only be given to companies…

In most countries these methods might be considered illegal, but it has been working absolutely fine for years in Ukraine. It is massively used nowadays too, and even more to that: you cannot run a business otherwise because competition would then throw you out of business very quickly.

The typical reason why you would get two bills is that certain products cannot be sold by legal entities with low taxation. Then you are billed for such food (esp. alcohol) by one entity and then you get another bill for the rest of your purchase from another entity. At certain cases the split is less clear because it might be not only about alcohol. I suppose that in your example hot chocolate is sold by the part of the shop known as “bar”, and the cake is sold by the part of the shop which sales complete products.

That is, it is not per plate billing as you supposed. It is rather a different kind of optimization when technically your purchase is provided by different “departments”. In most cases it is a sort of internal procedure of the seller and your asking to combine the bill just cannot help. The seller splits the bill not because they want to add fun of entering PIN twice but because they split goods and services for their own reasons, which cannot be changed on your request. More to that, waiters and people at the counter are not even necessarily aware of actual reasons behind the splitting.

Optimization goes way beyond the scope of cafes. In Ukraine you can find even a supermarket, which structured the business so that departments, that are obvious integral parts of the facility, are run as separate low taxation legal entities. If you buy stuff from different departments you can ask to combine the purchased goods as a single transaction, but it is obviously impossible: the sellers have their own goods to sell and neither of them could sell you goods from peer department.

UPD. By coincidence, there is a fresh (today’s) publication on check splitting: Two receipts in a restaurant // Два чека в ресторане:

… hence there are two businesses under the same roof: LLC sells alcohol and [low tax] individual entrepreneur serves food.

… if you happen to visit the same place frequently, you can also notice occasional business name changes. Is it a mistery? One individual entrepreneur approaches its annual limit on revenue, then he is replaced by a new one.

The article mentions various aspects of the expense optimization as well as the fundamental reason behind two bills. Interesting part is that the source of the comment is an ex-deputy finance minister. That is, everyone out there is aware of what is going on but there is insufficient motivation to stop the farce.

This is how they avoid taxes.

In Ukraine, there’s a special regulation for small businesses, called "Private Entrepreneur" (приватний підприємець or фізична особа-підприємець, abbreviated ПП or ФОП).
They have simplified requirements as per bookkeeping, quarterly reports, and — most importantly — lowered taxes and/or flat tax rate (contrary to a progressive one).
An important factor is that a small business is restricted with an annual limit for income, so one can’t run a big cafe/restaurant as a single ФОП.

So, a restaurant accountancy is "split" between several business entities, and usually, they do it by type of items sold, e.g., food, drinks, alcohol, etc.

If it happens that you ordered items which are "assigned" to different entities, chances are that your bill would be split in two receipts. Sometimes they "switch" at a certain time of the day, so if you order, eat, and order again several hours later, this can happen, too.

You can check the two bills, most likely they are titled e.g. "ПП name1" and "ФОП name2".

Source: I’m an Ukrainian national and a Private Entrepreneur (a conscientious one). 🙂

Also, can I ask the waiter to put the whole transaction together […]?

Well, you can try, but it can happen that their software can’t do that.
If you still insist, point at the two bills and try to say,
"будь ласка, обʼєдна́йте | в оди́н | чек" ("please merge | into a single | bill"),
here are three sub-phrases, you can use 1 or 1+2 or 1+3 or 1+2+3, depending on your Ukrainian proficiency (pronunciation).