It depends – the word "spore" has had a very broad application. But Apicomplexans, previously called Sporozoans, are one type of animal that produces spores. They changed the name partly because it was decided that spores shouldn’t be applied to animals, but in the protozoans you have species that have plant, animal, and fungus characteristics, so the term can’t be totally avoided.

Im am not sure that they changed the name because of "Sporo-". I would guess they changed it instead because of the "-zoans".

As you very rightly put it, the bunch of completely different lineages called protozoans (without a capital) have "plant, animal and fungus characteristics", and therefore are neither the one or the other.

Strictly speaking, only Metazoa (all multicellular) can be called animals. The definition of an animal is therefore something like "multicellular creature with collagen in its tissues"

Therefore, animals indeed do not produce spores (although they do produce sports and… bores)

Cheers

Dr D