The various reasons for why this happens are discussed here and here. I don’t necessarily agree with the reasons, but Jackson, because of type erasure, doesn’t off the bat know the type of elements the List (or Collection or Map) contains. It chooses to use a simple serializer that doesn’t interpret your annotations.
You have two options suggested in those links:
First, you can create a class that implements List<Cat>, instantiate it appropriately and serialize the instance.
class CatList implements List<Cat> {...}
The generic type argument Cat is not lost. Jackson has access to it and uses it.
Second, you can instantiate and use an ObjectWriter for the type List<Cat>. For example
System.out.println(new ObjectMapper().writerFor(new TypeReference<List<Cat>>() {}).writeValueAsString(list));
will print
[{"@type":"cat","name":"heyo"}]