The light, when closely encountering the matter in the slit is 'bent' or rather changes direction and explained as an interference between the light wave and the matter
Classically light is an electromagnetic wave; it is simple to understand waves when seen in water, for example. The sides of the slit are a boundary that force the wave to change direction and generate interferences because of the structure of what a wave is. It is the same with water as in the video , the classical view describes light waves too.
which also has wave-like properties.
Wave like properties of the boundaries do not affect classical water waves because the scale of a water wave and the scale of the quantum mechanical structure of the boundary slit differ a lot.
To understand where quantum mechanics enters, one goes to the quantum mechanical particles of light, the photons.
IN terms of particles, is it that the photons and matter both exert electromagnetic forces, and through these forces (and momentum exchange) the photon is diverted just like a billard ball?
No. Quantum mechanics describes all particle-particle or particle-field interactions with the wave function of the system under study. This is a mathematical solution of a wave equation, where the boundary conditions of the problem are introduced, the slit dimensions width. (For the wavelengths of visible light and the width of the slits in the usual experiments, the fact that the sides of the slit are made out of molecules can be ignored). It is a "scattering of a photon on a slit width" that will define the wavefunction , which is a function similar to the classical electromagnetic wave, because it comes from the same equation transcribed quantum mechanically. The difference with the classical case is that the wave function controls the probability of the photon to exist at (x,y,z,t). The wave function itself is complex, and thus unmeasurable, but it has the sines and cosines needed for interference effects to appear. The complex conjugate square of the wave function gives the real number which is the probability of finding the photon on the screen.
The scattering of the photon on atoms/molecules , which will happen on the sides of the slit, is elastic, it just changes direction according to the probability distribution. But because of the phases in the complex psi functions, this probability is not uniform but shows interference patterns as single photons are accumulated.. The same pattern calculated for the classical beam too, because there is continuity between quantum and classical solutions.
Diffraction is well modeled mathematically, and thus understood, both classically and quantum mechanically