If you ask me, I would define a singularity as an intelligent system capable of interaction with physical objects and intelligent systems. Such definition could be applied to whatever, although there is a scale of singularities: some are smaller/less powerful/making less influence through interaction/etc comparing to others. The term "intelligent" mainly means that such system can learn from experience (or else) and reflect herself and thus change way of interaction between herself, other intelligent systems and physical objects. "Intelligence" has its own scale(s)/magnitudes.
Singularity in my worldview might also be described by "event horizon" or rather horizons: certain limit(s) beyond which internal processes of singularity became incomprehensible for outside intelligent observer.
This morning I woke up with clear vision titled "singularity wars". Search for it brought me here. Although the post is old and not about singularity wars per se, I decided to leave a comment with hope to be led to a proper discussion elsewhere (or here). I assume (or rather visualize) that not one but number of singularities are already conceived and will born within a short period of time in a nearest future (within next 10 years). And instead of "clash of civilizations" will found ourselves in the reality of "clash of singularities". The nearest metaphor for it is this https://www.youtube.com/watch?v=ow9JCXy1QdY, only that the collision will take place not in physical, but in social space. "Existential risks" related to singularity wars are inescapable, at least with our current preparedness. Just for the reference: I live in Kyiv, capital of Ukraine, and the war we have now with Russia IMHO is not a "hybrid" but "proto-singularity" war.