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Correct me if I’m wrong, but objects (made of constituent atoms) glow with a particular frequency of light which our eyes relate to as colour.

They glow when a particle in a higher energy quantum state gets converted into a lower one by the emission of a photon. And the energy difference between the two states will correlate to the frequency of the photon.

So when we look at an emission spectrum we look at many colours being seen from a sample, now why are there so many (more than one)? Is it because there are many energy levels and the difference between this energy levels vary? Is it because of electrons being promoted and demoted from n=2 to n=1, n=3 to n=2, n=4 to n=3? But aren’t these energy states unstable also, won’t they all emit photons till they reach n=2?

Is that why irons em radiation is first within the infrared range and then progresses to the visible light range because the electrons are now in high enough energy levels that the frequency of the photons can be detected by our eyes?

They glow when a particle in a higher energy quantum state gets converted into a lower one by the emission of a photon.

That is one method of emission. Because individual atoms (and small molecules) have a smallish number of stable configurations, the types of emissions possible from the decay of a single particle is limited.

But in dense, high-temperature systems, the emission from an isolated particle is no longer dominant. Instead, the collisions and interactions between the particles cause charges (electrons) to be accelerated. Accelerating charges emit radiation, and this radiation is not associated with change in the atomic/molecular configuration.

Because there is no discrete configuration involved, just various rates of acceleration, the discrete lines of an emission spectrum are not present.

Matter comes in phases: solid, liquid, gas, plasma

Individual atoms/molecules join into lattices when solid, are in collective states in liquid, free in gas, and ionized mostly in plasma.

Transitions in the atomic energy levels you envisage are detectable only in gases and plasma, there the changes in n,l,m and the resulting absorption and emission of spectral photons can be detected, although there is also continuum photons from interactions in the spill over electric and magnetic fields.

In solids, there are a large number of energy levels that are lattice related, this means that there will be transitions in rotational and vibrational states that have nothing to do with atomic transitions. These transitions are the black body radiation, and are energy dependent. They also exist in the gas due to the kinetic energy . As you were told in comments this is the black body radiation, which characterizes temperature of a body. The higher the temperature the more photons in the visible.

Note the high temperature it is the high temperatures that gives us the observed light of the sun.

So yes, there are many energy levels , but it is the kinetic energy that dominates at high temperatures and gives a continuum of frequencies according to black body , or approximately ( atomic spectral lines can be filtered in a plasma, but it is the black body type of radiation that dominates).

Now for iron and metals in general the colors will barely touch the visible, as the temperatures are between 770K and 1480K