that’d be 4.5e39 kg of gases, or basically 500,000,000 times the current mass of the sun. So, at a wild guess, probably enough to form a black hole?

Yeah, the Sun is IIRC something like within an order of magnitude what would be required.

kagis

https://public.nrao.edu/ask/what-is-the-critical-mass-at-which-a-star-becomes-a-black-hole/

In general, stars with final masses in the range 2 to 3 solar masses are believed to ultimately collapse to a black hole.

EDIT:

https://en.wikipedia.org/wiki/List_of_most_massive_black_holes

Yeah, based on your estimate and that list, it looks like it'd make the solar system into something like the 90th-largest supermassive black hole that humanity knows about.

The center of our galaxy, the Milky Way, has a black hole that'd be dwarfed by what our solar system would turn into.

https://en.wikipedia.org/wiki/Milky_Way

he Milky Way[c] is the galaxy that includes the Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye.

It is estimated to contain 100–400 billion stars[30][31] and at least that number of planets.[32][33] The Solar System is located at a radius of about 27,000 light-years (8.3 kpc) from the Galactic Center,[34] on the inner edge of the Orion Arm, one of the spiral-shaped concentrations of gas and dust. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge. The Galactic Center is an intense radio source known as Sagittarius A*, a supermassive black hole of 4.100 (± 0.034) million solar masses.[35][36] The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.[37]

https://en.wikipedia.org/wiki/Sagittarius_A*

Sagittarius A*, abbreviated as Sgr A* (/ˈsædʒ ˈeɪ stɑːr/ SADGE-AY-star[3]), is the supermassive black hole[4][5][6] at the Galactic Center of the Milky Way. Viewed from Earth, it is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south of the ecliptic,[7] visually close to the Butterfly Cluster (M6) and Lambda Scorpii.

The object is a bright and very compact astronomical radio source. The name Sagittarius A* distinguishes the compact source from the larger (and much brighter) Sagittarius A (Sgr A) region in which it is embedded. Sgr A* was discovered in 1974 by Bruce Balick [de] and Robert L. Brown,[8][9] and the asterisk * was assigned in 1982 by Brown,[10] who understood that the strongest radio emission from the center of the galaxy appeared to be due to a compact non-thermal radio object.

The observations of several stars orbiting Sagittarius A*, particularly star S2, have been used to determine the mass and upper limits on the radius of the object. Based on mass and increasingly precise radius limits, astronomers have concluded that Sagittarius A* must be the central supermassive black hole of the Milky Way galaxy.[11] The current best estimate of its mass is 4.297±0.012 million solar masses.[2]

So the Sol system would instantly become about 100 times more massive than Sagittarius A*.

I don't know if all of that mass would actually wind up in the resulting black hole -- I assume that the collapse of all that nitrogen and oxygen and such coreward would induce nuclear fusion and a supernova would blow some of the mass of what had been the Sol system outwards.

Yeah, sounds like most of the mass may get blown away before some of the remaining can collapse into a supermassive black hole.