Let's not exaggerate. One cannot know everything. I can only speak of what I know and have explored over the years. The new "inventions," which are quite peculiar by the way, I do not believe are part of the "base" of the instrument.
I haven't tried Fazioli's "fourth" pedal, but I believe the same result can be achieved with other devices. It seems that "inventions" make our instrument appear more complete, more "complex," and therefore more interesting. Sometimes it is not so, and perhaps others "don't think about it" because they "don't believe in it."
As far as pedals are concerned, I see three.
The resonance pedal (sustain), a fundamental and ingenious mechanism that lifts the dampers from the strings and renews the harmonies every time we lift and lower it again. The release of the dampers obviously puts all the strings and all their partials into "sympathetic" vibration (it is necessary to have the piano well-tuned to generate a good effect). We learn to use it well or poorly "forever." Often, one is not taught how to use it, and we listen to pianists who use it only to create "confusion."
The purpose of this pedal's existence is mainly to "help" bind sounds together, but not only that.
From some "Schools," it is seen as the Devil and is almost "authorized" as a transgression. On Mozart, Scarlatti, or Bach, it can cause "scandal." Delaying learning how to use this pedal is equivalent to delaying putting on glasses... in the end, when it is truly necessary, you no longer reach 10/10.
One should learn to use it from the early years and understand that its correct use "benefits" Music.
There are various modes of use (on the upbeat, on the beat, syncopated, vibrato, off-beat....) but it would be more appropriate to discuss this use in a session on Performance Technique.
Its regulation is fundamental. In its stroke, it must have an initial "empty" part. This is to avoid generating "thumps" during its "rapid change." The end of the stroke must also be adequate. The dampers must "detach from the strings" just enough.
The left pedal, called "una corda," is so named in grand pianos because, by shifting the action to the right, it causes the hammers to play while excluding one of the two or three strings of the unison. This results in a weaker sound and a different timbre. Sometimes, to avoid modifying the latter, the displacement stroke is reduced so that the hammers play on three strings but on the softer part of the felt. In upright pianos, it is all different. This pedal moves the hammers forward toward the strings, creating an "empty" part of the stroke. This results in less impact force of the hammers against the strings.
The Una Corda (Tonale) is a true modern invention. And that is why almost all grand pianos have it. Everyone recognizes the great advantage of being able to lift the dampers for a single chord or a single note, leaving the related keys free, to play legato or staccato in other parts of the keyboard. Unfortunately, it is believed that this is only useful for isolating harmonies and chords that must be heard for a long time in the bass as a harmonic pedal (see the second page of Debussy's "Clair de Lune").
It is not just for this. I have seen this pedal used skillfully in the music of Galuppi or Scarlatti as a "discreet" resonance pedal. It can be of great help and effect.
In short, the best thing is to sit in front of our instrument and experiment. Dedicate some practice sessions solely to the pedals and the study of them.
Good Music
P.S. ...here we all help each other get out of the "pit"!!!!! And that is why we always lend a hand!!!! ๐