It's not really about syrups being required to have different types. Ironically, a 19th century dictionary exemplifies this quite well:
SYRUP: A SYRUP is a solution of sugar in water, previously impregnated by decoction, or infusion, with the medicinal virtues of some vegetable from whence it is named. [...] Syrups are bad preparations for children, on account of the sugar disordering the stomach and bowels by becoming acid.
— A Practical Dictionary of Domestic Medicine., Richard Reece. 1808.
"A syrup" here is about an (arbitrary) instance of a syrup, rather than about type.
It's about "syrup" being one of those nouns, like "paste", "lunch", "liquid", and "cake", that sometimes is countable and sometimes is not.
If it helps, the word comes from the Arabic word for "drink", and "drink" is also a noun that sometimes is countable and sometimes is not.
Observe the variability between countable and uncountable: Just as I can drink a syrup each morning I can also eat a cake for lunch (syrup being a breakfast favourite, and cake being a staple of my packed lunches), keeping my syrups in the refrigerator and my cakes in a cupboard, and preparing a lunch each morning.
This does not imply multiple types of syrup and cake, as they could all be raspberry and Battenberg for all that you know, just multiple instances of them.
This is actually a dictionary problem.
While the Cambridge Dictionary says uncountable, other dictionaries (e.g. Britannica, Collins) put this noun into the countable+uncountable class.