Be sure to enable the subtitles because he puts a lot of notes on the video. The descript also has a little essay about different common tuning arrangements.
That's utterly fascinating, I've never heard microtonal music before outside of older traditions like chanting. Some observations:
1) When microtones are used in the melody improvisation, it sounds totally natural because we're used to it with string bending in guitar. It's surprising yet satisfying to hear the same done on a piano
2) When microtones are occasionally used to make a chord "bluer", it's also very natural and satisfying as another flavor of dissonance, which totally fits with the kind of dissonant jazz we're already used to with piano
3) But when microtones are used for most/all the notes of the chord, such as the root... at least to my ears it sounds horrible, like the piano just went out of tune for that chord. Which makes me wonder if you could get used to it or not?
For #3, a lot of it IS jarring and often it is supposed to be... although in jazz there are no wrong notes, just bad resolutions (jacob collier). Oftentimes in microtone you will find a passage that sounds horrible at first but makes sense at the end, hopefully.
I think that you can definitely get used to it. It is a little weird to hear non-typical notes, especially if you have done any kind of pitch training, but at the end of the day it isn't the notes themselves that matter but their positions relative to each other in a chord or passage.
The youtuber I linked also has a bunch of Lumatone performances which is an instrument with a hex grid layout where you can change the pitch of a chord by shifting your hands up or down on the grid while maintaining the same hand shape. That approach makes some really good microtone music whereas a lot of straight piano layout players end up getting stuck in "ambient space noise" modes.
For your last point, if you just continued to adapt 12tet music into other systems I think it would continue to sound strange? Not totally sure, you'd get used to it to some extent but I think it would always sound noticeably off esp if you were familiar with the piece in 12tet like we are with this one.
But there are entire music traditions using other tuning systems and they sound "normal" to the people who grew up with them. Notably the 24tet used in arabic music but there are literally dozens of others around the world.
How are the extra notes entered? The keyboard looks regular, is there some note modification going on, or are the extra notes actually added as dedicated keys?
He's using software. The keyboard he is playing isn't the sound you're hearing. In the description he says he's using pianoteq. He also explains the process of changing from 12 tones in the description.
Be sure to enable the subtitles because he puts a lot of notes on the video. The descript also has a little essay about different common tuning arrangements.