What is the experimental evidence for a quantized EM field?
To my mind, the core experimental benchmark that really requires a quantized electromagnetic field to be explained is, as mentioned tangentially in the question, the Hong-Ou-Mandel effect.
The wavelike nature of photons, as displayed in the Hong-Ou-Mandel effect, is rather subtle ground, but let me start off with a statement that sounds controversial but really isn't:
Interference effects such as double-slit interference are not representative of the quantum-wave nature of photons.
This is somewhat amplified when seen from a quantum-optics perspective, but it's important to keep in mind that photons aren't "particles", much: what they really are is discrete excitations of the classical modes of the electromagnetic field. (You can then go full-circle and argue that all particles, from electrons to atoms in a BEC, are also excitations in a matter field, but that's a separate argument.)
As such, you only really start to be able to talk about photons in a way that is quantum-mechanically meaningful when you talk about counting statistics of a given state of light. Those counting statistics are, in a sense, 'riding' on top of the classical modes that they inhabit, and any interference features that those modes exhibit (like, say double-slit fringes or diffraction rings) are not really "the photon interfering with itself", they're just a geometrical feature of the mode that's being excited.
The reason I discount those interference features as unrepresentative of the 'true' quantum wave of photons is that there's yet another layer of interesting interference, and it is when you make those excitations themselves interfere with each other, in both constructive and destructive ways. This is what the Hong-Ou-Mandel experiment does: it combines the probability amplitudes of different combinations of possible excitations to rule out some of them,
Image source
in such a way that the light emerging from the beam splitter has a 50:50 split of the energy, on average, but this only ever comes in joint pairs of photons on each arm, and never as coincident photons on both arms (an outcome whose probability amplitude has vanished through destructive interference). There is simply no semiclassical model that can account for this.
Now, as OON has noted, you can also get experimental observations of photon-counting statistics that are not explainable by any semiclassical model by simpler configurations of sub-poissonian light, but for me the Mandel dip is much more striking, much more clearly recognizable, and not that much more recent historically speaking.
Also, I would like to address some the comments in anna v's answer. All light is quantum; we know this because we've tried repeatedly to find cracks in quantum mechanics, including its treatment of light, and we haven't found any. Light often 'looks' classical, but that is only because quantum mechanics, in its classical limit, looks like classical mechanics.
However, there is still a lot of value of which experiments can still be explained by having a classical electromagnetic field (so, e.g. replacing coherent states with just classical states, possibly with some shot noise) interacting with quantized matter, and this includes things from atomic absorption and emission spectra to the photoelectric effect, as well as the pointwise response of film in double-slit experiments (whose interference features, again, are just a classical-optics feature of the mode that photons are riding on).
Given what we know of the fundamentally quantum nature of the electromagnetic field (through experiments like the Hong-Ou-Mandel dips), we know that these semiclassical descriptions are just effective models that don't fully describe the core aspects of nature, but it is those experiments that are undescribable without quantized fields that really force us to adopt that perspective. Take those away, and saying "the EM field is quantized" becomes just an opinion without meaningful experimental support.
Most direct example I know of: You can simply measure the number of photons that there are in a cavity (a 'light box'), by sending an atom through and measuring its phase change.
This has been done and published in 2007 by Gleyzes et al.: https://www.nature.com/articles/nature05589
The Hong-Ou-Mandel effect mentioned by Max Tyler in the comments is another great example.
The classical electromagnetic field is emergent from an enormous number of photons, and that can be proven mathematically.
Experimentally the simplest demonstration is the emergence of the double slit interference pattern one photon at a time:
Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.
One sees the individual photon leaving a footprint that looks random, but is not as the phases of the photon wavefunctions in superposition build up the classical interference. One uses this sequence to stress the quantum mechanical, probabilistic wave nature of the photon wavefunction
This pattern is explained by both QED and classical electromagnetism.
Yes, Maxwell's equations for light are very useful and it is not necessary to go to the underlying quantum level, because the mathematics is consistent. Only for absorption and emission spectra the existence of photons is absolutely necessary, and the photoelectric and black body radiation of course.
As far as semi classical claims go, the "semi" is indicative of phenomenology fits, which is fine for fitting data, but not an argument against the underlying quantization.