What does a "forming" black hole look like?

This might be a silly question, but something made me think about it recently...

Let's assume, as a thought experiment, I filled a spherical volume of space with a radius of 77 AU, with "air". By "air", I am assuming "matter that has the same density as Earth's atmosphere at STP" ($1.293$ $kg$$/$$m^3$). Let's also assume, for the sake of the experiment, that the matter was also transparent, (instead of scattering/blocking light), so that we can see what would happen at the centre of this spherical volume.

Also assume that the "Air-Bubble" was assembled instantaneously, and since it does not need to be a standard baryonic gas, we can ignore the "collapsing into a comically-massive (and short-lived) protostar and releasing tons of heat" part. You can treat it as a ball of really dense dark matter or similar types of matter that don't interact much with EM radiation.

According to the hyperlink above, such a volume of "air" would have a mass of around 3.9 billion solar masses, and this is the part where it gets interesting.

The Schwarzschild radius of a body with a mass of around 3.9 billion solar masses, is around 77 AU. Which means that theoretically, after it reached that much mass, it would automatically form a black hole.

What it would look like, has really baffled me indeed.

I know that from the perspective of an outside observer, an event horizon will take an infinite amount of time to form. However, this answer from the Physics Stack, about an collapsing neutron star, states that instead of an event horizon, an apparent horizon will form in a finite time for an outside observer, which would be so identical that you couldn't distinguish between an apparent horizon and an event horizon.

However, the same answer talks about a collapsing neutron star, which by the way, is a few miles across and given its small size, an apparent horizon will form within microseconds for these black holes. On the other hand, the volume of space, doomed to become a black hole, is about tens of AUs across, which according to my limited understanding would imply that an apparent horizon would take much, much longer to form for this large volume, although my understanding might be wrong.

For detecting the formation of this horizon, assume I had a bunch of illumination points, say 10-50 stars with negligible mass (negligible with respect to the black hole's mass), arranged in a radial manner from the center of the volume, and was standing at a safe distance (a quarter or a half of a light-year away), would I see:

A dark sphere (the apparent horizon) expanding outward from the centre of the volume at the speed of light, taking a few hours to reach the Schwarzschild radius? This would mean that the stars nearest to the center would be the first one to disappear (Well, I think they would actually be redshifted to infinity, but here, if they get redshifted to really, really long radio-waves, below the thresholds of human vision, that technically qualifies as "disappearing"), and the stars further out will disappear at the last, being engulfed by a wall of expanding blackness.

A black wall forming on the surface of the "air"-filled space first forming in dark "patches", then finally engulfing the entire volume at once in a few hours/days. Meaning that you could see a few stars inside, while the others would suddenly get obscured by opaque black patches, till at last the apparent horizon forms, and it all goes dark

Or the apparent horizon forms faster-than-light, and suddenly our volume is engulfed by a "black sphere", meaning that all the stars inside this volume, suddenly disappear at once. Since the formation of an event/apparent horizon is an event that "disconnects" the engulfed space from the rest of the universe, and does not cause matter to move, I don't see why the formation of a black hole can't be FTL, though there might be a flaw in this understanding, so feel free to correct me.

Or in a more, realistic scenario, assume the formation of direct-collapse black holes in the early universe, which could form from gas clouds hundreds of thousands of solar masses collapsing directly into a black hole.

Assuming we had an indestructible observer and a indestructible slow-motion camera positioned at the outside of the collapsing gas cloud, and assuming the observer viewed the slowed-down footage later on, would he observe a "black sphere" expanding at near light-speed till it reaches the Schwarzchild radius, or formation of "dark patches" on the surface of the "would-be" black hole, slowly engulfing the volume to be occupied by the apparent horizon. Or would the black hole appear to form instantaneously?

Assume an indestructible cameraman with an equally-indestructible slow-motion camera, being able to film frames picoseconds-long, submerged into the heart of a massive star whose core will collapse into a black hole.

After he observes the core collapsing into a black hole and records the event (too fast for his eyes) he exits the star and reviews footage from his camera, frame-by-frame, in slow-motion, would he also observe one of the scenarios occuring as outlined above?

The first scenario here is hypothetical, but the question is not directly linked to the hypothetical scenario, because my main question is not about how you could get such a large "air-bubble" to form in the first place, or how did I place a bunch of stars in a radial manner in that volume. My question is regarding the appearance of a "forming" black hole.

There's no physical way to bring a 77 AU ball of air into existence without starting with some distribution of matter that's larger than 77 AU and collapsing inward. That means it's going to have a more dense area in the center and a less dense area on the outskirts, not a smooth 1 atmosphere of gas all the way through. And the collapse of a huge mass of gas is going to cause heating, so you're going to be dealing with glowing gas around a small black hole that's growing as it consumes the in-falling matter, which will self-organize into an accretion disc. Asking "what would happen if" about a scenario that can't happen is kind of fundamentally impossible to answer properly.

If we somehow avoid the "protostar collapses into a black hole" scenario and just sort of magic the matter into existence, there wouldn't be a time when the mass is beyond the schwartzchild limit but isn't a black hole yet, so the moment of its appearance would be accompanied by a dark circle popping into existence (an area of the sky from which no light can reach you), rimmed by a huge distortion as all the light coming in at near-tangent to the new event horizon encounters a mass that bends its path in crazy ways.

Assuming we somehow set up a starting scenario where we have a bunch of cold, transparent gas that is nearly a black hole but not quite there yet, the existing gas cloud is going to be accompanied by huge gravity distortions, because you have a near-black-hole density of mass bending light around it. As the final collapse past the limit happens, that distortion would become more and more extreme, and the light passing through what's about to become the event horizon would red-shift out of visibility.

So, I think the answer you want is this: What you'd actually see as a black hole forms, if you could watch it happen without being blinded by glowing matter, is the image of objects around the forming black hole bending and warping into smeared-out blurs. At the same time, light passing very near or through the incipient black hole would be getting redder and starting to fade away as it shifts fully into the infrared, then into microwave and radio. That fading leaves the dark space that represents the "surface" of the black hole (i.e. all the directions that light cannot possibly travel through to reach your eye), rimmed by rings of light that are the objects around it being stretched by the bizarre combination of light paths that can lead from them to your eye.

There can't be a spherical region with a radius of 77 AU filled with matter with the density of air, because the only possible object of that size and density is a black hole. You ask us to assume that the matter was assembled instantaneously, but that isn't possible either. That isn't just nitpicking. It's fundamental to the geometric interpretation of gravity that the matter at any spacetime location got there from somewhere else, bringing its gravitational field with it. The field is always present from the beginning of time.

There can be a sphere slightly larger than 77 AU filled with air-density matter and some light sources of negligible mass. That matter will already have a huge gravitational field, not quite at the level of a black hole but close. The internal light sources will consequently appear from outside to have a large gravitational redshift. As the matter continues to collapse, what you'll see from outside is the smooth continuation of that process: the light sources get more and more redshifted until they're invisible. The decay of the brightness is exponential, with a time constant comparable to the light-crossing time of the region, i.e., roughly 1 day in your first scenario. There is no moment at which you see a growing sphere, or any other discontinuous sign of black hole formation.

What you'd see in all three scenarios is the same: a gradual fading of the doomed matter into invisibility.