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I'm interested in the grayscale image case.

In a sensor there is an array of cavities which collect photons.

Does each cavity count the number of signals(or peaks) generated by each photon or is there one signal which is the sum of all photons (in which case the size of the signal should depend on photon energy presumably).

And also I'm guessing each cavity correspond to a pixel?

source:
https://www.cambridgeincolour.com/tutorials/camera-sensors.htm

some sources/references would be useful thanks

No, you won't obtain the photon count directly. Also, a camera sensor has noise, not just from photon counting but also from electrical circuits.

Also, a DSLR has a color filter on top of the pixels, even if you take only grayscale images. It will probabilistically filter away some photons. If the photon is of the correct color, chances of it passing the filter are much higher than with an incorrect colored photon.

There are sensors that count incoming photons, but a DSLR sensor is not among them. DSLR sensor just gives a single "intensity" value per pixel that is full of noise. It is roughly similar to sum of all incoming photons, but because of the noise, you can't tell the number of photons exactly as an integer.

If you are looking for a photon counting detector, this may not be the best place to ask. There is no Scientific Instrument Stack Exchange, but Physics Stack Exchange may come close.

Typically, photon counting detectors are cooled with liquid nitrogen to really low temperatures to minimize electrical noise coming from thermal effects. Needless to say, a DSLR isn't designed to be cooled to such low temperatures.

At shorter wavelengths such as X rays, you can actually count photons using a room temperature sensor, so no cooling required. However, light has far longer wavelength than X rays. I'd say it would make a great question on Physics Stack Exchange to ask whether a visible light photon counting sensor can be made without requiring cooling.

The sensor is an array of silicon photodiodes that simply convert light energy into electricity.
They are interchangeably called pixels, photo sites, photo diodes. Pixel actually refers to picture element and it is the least accurate term in this aspect. Because each pixel uses information from adjoining photosites to determine its' color/brightness value, even for greyscale output (other than possibly a monochrome camera like the Leica Monochrom). But the location of a photo site does directly correlate with the location of a pixel in the output image.