The problem here is that there are actually three very different meanings of "coherent" that are getting conflated, and it is unfortunate that the term is used in so many different ways, all related to the concepts of "phase" and "interference."
If you consider a single photon, then we can use a wavefunction to describe its behavior. That wavefunction, as mentioned above, will have a "coherence length" (which is infinite for a plane wave of definite frequency, but actual photons have wavefunctions that depend on how they were created, and have a finite coherence length). The coherence length of the wavefunction has to do with the time t it took to create the photon, and then ct is essentially the coherence length. Within that length, the photon wavefunction can interfere with itself, and produce the slit patterns you are talking about. This would be true even if you are only observing a single photon.
A second meaning has to do with radio detection, where you have so many photons that you don't actually detect the photons at all, you detect the classical field they produce. In fact, you think of the creation of the field directly, so you never think of photons at all, you just solve the classical electrodynamics equations. This ends up being very like the wavefunction, because the amplitude of an electromagnetic field has similar properties, including a coherence length. So radio detection amounts to correlating fields at different places in the detector, so you are detecting phase differences due to different propagation lengths, i.e., you are detecting an interference pattern in the field amplitudes, not a photon flux (though you could reconstruct a photon flux if you wanted to, you just have no reason to).
But the meaning in the OP is quite different from either of those, it relates to the photon distribution and its occupation numbers. What is meant by "coherent radiation" here is that the brightness temperature is very high because the occupation numbers in the photon modes you are observing are significantly above unity, i.e., it strongly matters that photons are bosons. These photons are "coherent" because they are all in the same state, so have the same phase not just the same energy.
Indeed, you can associate a thermal spectrum with a brightness temperature by looking at what photon energy do the photon modes have occupation numbers above unity, and associate that photon energy with kT, where T is the brightness temperature, and it will be similar to the local temperature for a blackbody radiation from a stellar photosphere. But lasers pick out special states and put lots of photons into those individual states, driving the brightness temperature way above the local temperature. This is why lasers are good at cutting things-- you can get a lot of energy into the photons because of the constructive interference that comes from adding amplitudes in a coherent way (which is what puts the photons into the same states). In effect, what you have is a source of amplitudes, not a source of photons per se, and when you add the amplitudes coherently (because you are selecting the same photon state), they add up to very large amplitudes, which in turn causes there to be a large number of photons (you get a high brightness temperature and high energy efficiency from a laser).
The way to tell if this is happening in a star is to look at the processes that create the photons. Photons are created by a feedback between how the creation of a photon produces a field that resonates with the process creating the photon. "Coherent" processes mean that the stimulating field is due to photons that already exist, called "stimulated emission", whereas a more typical process is when the stimulating field is from a virtual photon that does not yet exist, called "spontaneous emission." So what is meant by coherent radiation from stars is when you have most of the light you are talking about coming from stimulated rather than spontaneous emission. But stimulated emission is also associated with scattering and absorption, which reduce the brightness temperature, so the trick to getting "coherent" radiation is to maximize the stimulated emission and minimize the scattering and absorption, which requires "population inversion." This means you have a higher population in the upper level of the atomic or molecular transition that is creating the photon, which gives you "amplification" (the "A" in LASER and MASER) because it gives you more stimulated emission than scattering or absorption.
In short, to have coherent emission of the type implied in the OP, you need to "pump" the upper levels of the transitions, so they act like a laser. This can be done by radiation at other wavelengths, as mentioned above.
