Taking all this into account on could say the una-corda pedal can be used as a kind of equalizer, changing the timbre of the tone. Like a sound engineer when doing the master mix after the music has been recorded. The pianist does it in real time, while playing.
What do we do to make the music sound the way we want it, the way we think the composer wanted it? What techniques, what tools do we use for our performance?
Pianist are funny people: first they choose an instrument which is basically a percussive one, striking strings with a hammer. Then they spend most of their time practicing to make the audience forget that fact by trying to produce a beautiful tone and make the instrument “sing”.