There are spoons specifically for the sugar bowl. They are called sugar spoons and are often scalloped.
That is correct.
what can be objected afgainst
i drink the coffee with a spoon of sugar
The English expression is "a spoonful of sugar"
It is "my coffee".
Is there a way to say "a sugar spoon"? As in a spoon that's specifically used for sugar? Maybe I come from a bougie family but I'm family certain that can be its own object.
I haven't ever heard of this, but, purely grammatically speaking, it would be either "κουτάλι της ζάχαρης" -or- "κουτάλι για ζάχαρη".
(I am not an English native speaker) I don't understand why was not accepted "a spoon of sugar".
A lot of English is based on how words are used together. In this case, we say "a spoonful".
There is no grammar involved it is just the way the language is. You'll get used to it and of course, ask us anything you don't understand.
A teaspoonful is a spoonful in this context at least in UK English
It could also be a "tablespoon" and I mean in the UK.