The most reasonable interpretation so far
Here is some analysis to supplement the parts that may be forgotten or ignored by players - in fact, at the beginning, both Floro and Drifter himself thought that Drifter had missed the appointment.
It wasn't until finally that Floro was stabbed by the drifter that she finally discovered during the fall that the original agreement could only be fulfilled at this moment.
Floro said that the violin was the most perfect gem, and it was given to Floro by everyone in the village. But she couldn't find a violin, so she had to replace it with a gem that carried the power of Liviatan.
When the drifter went to the other side of the lost shore to pick up the violin in the water, he was pulled into the seabed.
After being pierced in the chest by a drifter and falling off the platform, Floro also fell to the bottom of the sea, only to find the violin, at which point she no longer needed the power of the gem.
Floro picks up the violin and plays it, and when the people around her appear, she actually finishes the piece (she has always wanted to put the villagers' full frequencies into it).
The sorry words that Floro said were actually said to the drifter, and when she fell to the bottom of the sea, she finally realized that without the drifter, maybe she would not have found the violin at all, let alone completed her movement.
As for why the violin can replace gemstones, Floro said that if you want the other side to be in this world, there must be a clear "texture", but she has always been misled by the Remnant Star Society, thinking that the "texture" is a gemstone, and she has never thought that the real "texture" is actually the violin.
And the sea of energy that Floro finally fell into is the sea of energy under the "Tower of Surge" on the map, perhaps the energy here is comparable to that of Leviathan in the gem. When we go there again and look down, we will find a thick fog.
So after Floro fell, the drifter actually couldn't see what was going on underneath Floro, the drifter's eyes closed may be silent, maybe heartless, but more unknown, but more important than confirming Floro's situation, more important is the unsolved mystery about Finlake in front of him, so he doesn't have time to think about Floro.
After talking to Finlake (Fenrico), Drifter saw the petals on the other side again, with a surprised look, which made him realize that Floro was not dead, so he told Abu that there was still something important to do, in fact, this important thing was to go to the appointment.
At this moment, Floro's movement has been completed by the texture of "violin", and Drifter also needs to fulfill his promise ("I will definitely come again when your piece is really finished. So after the end of the chapter, the drifter can enter the other side of the lost on his own.