Amplitude noise vs Phase noise
This is kind of misleading. The blue line is the noise floor. Signals below the noise floor cannot be seen as peaks on the plot.

The carrier (if there is one) has a peak, and it falls off as you move away from the peak. A perfect sinusoid would be a straight vertical line. But in reality, there is variation in the frequency, and that causes the carrier to have a spread out shape.

So what you are calling phase noise is just part of the signal that is not at the center frequency. Basically, the statement that "phase noise dominates close to carrier" just means that the sloping sides of the peak are above the noise floor.

Phase noise is related to jitter or spectral purity. It isn't noise in the same sense as the noise floor.