dnd 5e – What’s the definition of an artifact in regards to a Sphere of Annihilation?

An artifact is an unique magic item of divine (or equivalent) power

Mechanically speaking, “artifact” is special category of magic item. In addition to being the absolute highest level of rarity, even rarer than “legendary”, there are also special rules that apply to all artifacts, most of which are detailed in Chapter 7 of the DMG. The most relevant to this question are the rules for destroying an artifact:

An artifact must be destroyed in some special way. Otherwise, it is impervious to damage.

So, unless “throw it into a sphere of annihilation” just happens to be the special way to destroy a specific artifact, that artifact cannot be destroyed, or even damaged, by a sphere of annihilation. This kind of exception is common for artifacts. For example, Antimagic Sphere also has no effect on artifacts.

Lore-wise, most (all?) artifacts are items created directly by a deity or something of equivalent power, which explains why they are impervious to things that would suppress, damage, or destroy most magic spells and items.