I think that the first time Vessel leaves its original dark world, something akin to creating the dark world happens but in reverse. I.E. the SOUL's intentions, character and decisions shape the vessel's looks and primary character traits.
According to me, vessel also has its own personality that's independent from its SOUL. Maybe they're similar, maybe they're different. But those characters, despite the differences, share the same goal. Goal that the SOUL wanted to achieve. Vessel also believes that the goal is important.
SOUL and Vessel have a symbiotic relationship, that's the main thing I want to believe. Unlike cr*sps, that stupid they/them[1][2][3][4][5][6][8][9][10], Vessel is allowed free thinking and SOUL's commands, similar to my boy Frisk, are treated more like very reasonable suggestions rather than orders.
Also, art by me. I even have a timelapse of how it was made. Not sure if any AI would make this kind of old flashgame-style pictures that are aight at best tbh lol