Piggybacking on this, I got the impression that the shroud was just raw investiture (the remnants of the original people) that the machine was using to repair itself. There’s a quote when Father Machine dies that references most of its physical body was at that point made of the shroud, and those pieces deteriorated/evaporated once it turned off. We also had Design directly state that matter, investiture and energy are ultimately the same and can convert between phases. We also know that as a highly invested entity, Yumi has the direct ability to control and manipulate the shroud, as well as feed off/absorb it (Design says it, and she does it at the end with the scholars).
As mentioned above, the shroud itself dissipated over a short time, not instantly. I got the impression that Painter and his art called to Yumi’s cognitive shadow/spiritweb, and served as an anchor. Then Yumi’s inherent power allowed her to control the remaining shroud in the area (aka raw investiture) and create a physical body linking her cognitive and spiritual aspects from the raw investiture (which we know she can control), so she is anchored to all three realms.
I don’t have an answer to why, if she’s made of shroud, she didn’t dissipate with the rest, but it is implied that her control of the shroud is even greater than Father Machine’s. Maybe her willpower is enough to retain the shroud/investiture that makes up her new body.