If you're talking about FFVII's Singularity...
Everything in FFVII to do with the Lifestream *is* magical. Or rather... the Lifstream is made up of magic energy, where everything is born from and everything goes back to. "Magic" is just interacting with parts of the Lifestream in different ways while alive (and also dead). The Singularity was... obviously magical from the get go given stuff in the Lifestream was involved in making it.
"Magic" in most FF games (even earlier ones) is a really bad term for the "energy manipulation" that goes on in them TBH. Most FF Magic falls under the
Magic A is Magic A trope, that is their magic rules are logically consistent with themselves. Some FF Magic systems go so far as to turn "magic" into
Sufficiently Analyzed Magic where "Magic" might as well be a branch of "physicis" in those 'verses. It just becomes yet another tool for people to use get predictable results.
If you're talking about Singularities in fiction in general... In Sci-Fi works, they're some kind of unknown physics most of the time. This goes back to "black holes" IRL and how they were originally "discovered" by mathematicians playing around with the General Theory of Relativity and found some place that the math worked out for enough mass to be gathered in a single point for "space time" to warp around it so much that light could no longer escape. Essentially Mass becomes infinite while it's "dimensions" goes to Zero and you wind up with something that is mathematicly impossible... but still completely allowed by the General Theory of Relativity. Phisicists kinda hoped this was just a mathematical problem and didn't exist in the real world until... it turned out that the universe was actually cool with this idea and Black Holes are totally a thing that exists IRL. It's just that *no one* gets how they really work due to how they can't "see" them thanks to light not being able to escape... There's a whole bunch of physicicts who would *love* to get some better working physics models that could clear up the math issues of them. But so far... they've come up with nothing recently...
In fantasy, it's a lot more simple. Just get whatever magic works in a particular setting to make pocket dimentions and make one that is "curved in" on itself and cut off from the rest of the "main" dimention in some way. Usually they're bigger on the insdie than the outside due to Singluarities being in a single "point" in space. The Tardis is... a pretty good example of a "fantasy" singularity for all that it's in a (very soft) sci-fi setting.
The other thing to say about the Singularity is that it's
a (philosophical) concept and trope in it's own right. You'll see it used most often to described Technological Singularities (often in speculative fictions), but at it's core, is a very simple idea. A "singularity" refers to a point in a system past the point of which, the normal rules of that system no longer apply. There's usually some sense of things happening the system that stress the system in some way that it ends up breaking. In the case of a physical "black hole", it's the physical laws of gravity and space-time that no longer apply and matter as a whole that ends up breaking down.
Or as the
laconic on the Singularity trope page puts it.... "Accelerating change goes asymptotic, things get crazy."
Which is a really good description for what happens in FFVII Remake with the changes the Whispers are trying to stop. The changes start out small in scope and relitilvy few... and then keep compounding on each other in scope and effect until Cloud and Co. wind up at the "Singularity of Destiny"; a place where the normal "rules" of Destiny don't work and everything is crazy. There they kill "Destiny" as a concept thanks to the broken rules that don't apply to them in the Singularity.
Remake seems to be playing around both the physical/mystical type of Singularity and the philosophical concept of a Singularity all at the same time/place.