So we switched towards focus on musicality. We greatly slowed down the progress of learning new melodies. And we review old pieces by adding appropriate dynamics, staccato, legato and other small elements.
It seems to be a complete disaster. Lucas (my son's name) has no interest at all in replaying these simple pieces in different style. Lucas has lost initiative in practice at all. Now we have to push him for every session.
I think that's a sign that one should backtrack. Keeping a child's interest so that they are motivated to play the piano 10 years hence is so much more important than trying to attain perfection right now. Technique can be corrected and musicality can be developed later on, but once someone loses that interest, it can be very hard to proceed.
From a child development perspective, I think that children develop certain things at different rates. Just because they have developed one thing quickly doesn't mean that they should be treated like someone older than their age. It depends on their natural inclination as well.
There are children who are interested in musicality while not caring about technique, and vice versa. These things can be developed later on, and it's probably counterproductive to try to force something too early which will automatically come about in a few years.
Online, we see videos of prodigies or very talented children who start young and learn everything correctly. But this is rare, and not just because of lack of effort. Those children naturally understand much more than your average child, and so a routine like that works well for them because it builds upon what they already understand and want to achieve. Now, I can't comment on specific cases, but it's just something to keep in mind.
It appears like your child enjoys the physical challenge of coordinating both hands, and enjoys the sensation of playing. That is a very good thing, and I think it should be possible to approach teaching from that perspective, and gradually ease him into playing more musically rather than the converse.
For example, one thing I like to do when I demonstrate things to people is pick an appropriate piece of music which makes that thing inevitably come up. For example, you could pick a difficult fast piece which feels great under the hands, but which is simply impossible to play with a lot of tension. You can pick a piece which makes a certain fingering choice way better than another. You can pick a piece of music where a grand crescendo is a very obvious way to interpret it. What exactly you do will depend on the individual.
It is a super hard journey trying to let him relax her fingers, wraists and arms. Fundamentally he only knows one single technique which is pressing the key firmly. We have a diffiicult time to lead him to play softly, to relax fingers after touching the key, to play the legato with the sense of flow. The obstacle is much greater than I anticipated.
This is one of those places where suggesting harder pieces can be appropriate, if the child takes to that well (some get frustrated by it, some take it as a challenge). I think teachers often teach methodically and rather dry, afraid that they will ruin something in the child's technique if they learn anything wrong. I'm not necessarily saying this is wrong, but I often see people burn out from this sort of teaching. I know I would. In a way, I'm glad I taught myself advanced pieces and all the basics back in the day, because it makes it so that I'm never afraid to take on a challenge.
Basically, the harder a piece gets, the more impossible it becomes to play simply with firm fingers. What if you have jumps? Fast arpeggios? Some people might stick to trying to apply whatever they know and constantly fail, and I have seen this. But I think many realize that other approaches work better and once that realization comes about, set about to incorporate those techniques gradually in their own playing. I feel like this would be more appropriate to a student who is a sort of technical experimenter. The trick is to provide as much context as possible to make the realization as natural as possible.
I think those concepts are just too advanced for him. I also struggle outside of the piano lessons. I tried to get him more exposure but he does not even listen to music.
Keep in mind that children passively pick up music most of the time, much like language. Even without a clear indication that he's paying attention, he might be listening to whatever music is playing at home. This is far more true for children than for adults. But of course it depends on the individual -- I recall that as a child, I knew way more music than most people realized because I would pick up whatever songs were played by people or on the radio, or by my parents without even thinking. After a few years, musicality will automatically increase in many cases, with experience.