I mean, honestly, most things in astronomy are highly uncertain. The rare certainties are prized and treasured.
The part you quoted is about the magnetic field’s density and not the bulk star’s density, so I’ll start in that context.
The field is way denser than lead, but density isn’t the determining factor in black hole formation. A black hole does form when enough mass is located in a small enough region, but how much mass you need in the region is connected with the region’s linear size and not its volume (which is how density scales).
More directly: the magnetic field here has an extreme density, but this strength of field would need to span a much much bigger region to have enough total energy (within that much bigger size) to warp spacetime enough to be a black hole.
Another example to show how the “mass to size” scaling matters: Earth weighs 1025 kg. If you crammed all of the earth into a 1-m3 box, the density there would be obviously 1025 kg/m3 – way, way more than anything discussed above. But it would not form a black hole! There is a lot of density there, but the box is also not very big, so this box-Earth would not form a black hole. If you used a box 100 times smaller on each side, then the density would go up by another factor of a million while the linear size would only change by that factor of 100. That would be enough for a black hole.
When the density is governed by real physics – like with the neutron star or its magnetic field – you need the densities to exist over large enough volumes to get a black hole.
For the neutron star itself: There is a fairly narrow range of stellar remnant masses where a neutron star is the resulting stable configuration.
If too light, the remnant is held up from further gravitational collapse by electrons serving as a maximally compressed quantum gas. The Pauli exclusion principle forbids them from being squished any further.
For remnant masses above 1.4 times the mass of our sun, the heat of this attempted compression is enough to cause electrons and protons to combine into neutrons, removing the electron back-pressure and allowing further collapse. The newly formed neutrons represent a new quantum gas that will compress as far as it can again – down to a much smaller size than the white dwarf – and this is a neutron star.
The maximum mass for neutron stars is around 2.5 times the mass of the sun, give or take a good bit given present uncertainties. But that 1.4x – 2.5x range is pretty narrow. Beyond that mass range, the neutron back-pressure also fails, and the star collapses to a black hole.
This generally all happens right at the time of remnant creation, as in a supernova explosion. Which is to say: neutron stars by their very nature are just those remnants that happened to land in this mass range. There are plenty of remnants out there that “could have been” neutron stars but instead became black holes due to too much mass.
Also note that it’s the mass of the resulting neutron star that matters, not (directly) the mass of the original star. Most of the mass of the original star gets blown away in the supernova explosion (though of course there’s a relationship between the size of the remnant and the original size).
Also, it’s actually still electron degeneracy pressure that supports a neutron star. Most of the baryons get converted to neutrons, but not all: Around 10% remain protons, with the corresponding electrons still present.
The stellar mass that could be supported simply by the residual electron fraction is very small. If we do move away from the approximation of “all neutrons”, a lot of complexity comes in all at once, but neutron degeneracy pressure remains a key ingredient.
The first big addition to the picture is that neutrons are interacting particles, and those interactions play an important role in stability of the star. With neutron degeneracy alone you can support about half the mass, and most of the rest comes from nuclear interactions.
But the neutron star is also highly stratified, with pressures varying from “small” on the outside to “ludicrous” at the center. So, the very outer layers are rather mundane, and the transition from that to the neutron-rich bulk crosses intermediate layers rich with ions and where electrons are in a degenerate gas, but this is not a globally supporting stratum but just one part of the thermodynamic equilibrium of that layer. Inside of that, there are neutron-rich nuclei and then higher and higher neutron fractions, until its a degenerate neutron gas. (And then possibly you reach some further exotic form of quark-gluon matter at the very core [speculative], but even then the neutron-rich, stellar-supporting bulk is still required.)