I wondered what the extra pedal on some grand pianos is for. Now I know.
No, that's not the one! That's the so-called "sostenuto" pedal. My piano only has the two, the sustaining pedal, which lifts all the dampers off for extra resonance, and the una corda (one string) or "soft" pedal. That shifts the entire keyboard and action slightly to the left so that a different bit of the hammer's felt hits the string. Technicians talk of "voicing the una corda" which means they stick tiny needles into the felt of the hammers so that bits of it are softer than others. I think it must be a very intricate and painstaking job. On an upright piano, rather than sticking needles into the felt, all the hammers are pushed closer to the strings so that it is possible to play with more delicacy. This means that it is possible to ensure that the hammer hits the string at a lower velocity, thus the sound is less.
The sostenuto pedal enables the pianist to hold down a chord and if the sostenuto pedal is then depressed, the dampers of just those notes will be held back even when the keys are released. This enables some notes to be held on whilst the fingers go and play a load of other notes elsewhere. I believe this innovation was introduced by Steinway in about 1910. I have rarely played a piano with a third pedal* and never had cause to use it. The only pedal you use regularly is the sustaining pedal. The pedals are normally made of brass and you can tell how much use the piano has had as the sustaining pedal will have been worn down by decades' worth of shoes pushing it up and down.
*When we were in Vienna last year, we visited a piano showroom in which a Feurich grand had a 4th pedal fitted. That does something a bit weird, and makes the piano sound as though it's in a rickety old cathedral.
The bluetooth pedal is something with a built-in battery which just sits on the floor to my left and I give it a shove with my left foot at the right time.
A year or so ago Jan and I attended a concert at the Bridgewater Hall in Manchester in which the soloist Lars Vogt actually had an iPad inside his piano! He was using his left foot to turn the pages, although I was rather surprised that a virtuoso would not have memorised the piece. It was Beethoven's 4th concerto, so very much part of the standard repertoire.
Edit: here's a video demonstrating the harmonic pedal. Feurich is an old make of piano and the name has recently been reintroduced by Wendell & Lung.
https://www.youtube.com/watch?v=t7z6cYWjr3Q
