Yeah, it is kinda amusing that one of the stablest ABIs for GUI applications on Linux is the Windows one :-P.
Sadly the Wine GUI controls, while they work, always felt off to me and have multiple minor issues. But at least they work. I think a big reason is that despite libwine being usable as a general purpose toolkit for (ELF) Linux application, it never saw much use as that so these issues were never paid much attention.
Vulkan would make things more complicated and wont really fix anything (if anything it'll make things worse because that added complication will make it harder to fix things and most likely will break compatibility with anything not supporting Vulkan - e.g. older and/or weaker devices and other OSes like macOS) since it isn't really rendering that is the issue but behavior (there are also some drawing issues but those are at the GDI level and you do not want to break GDI).
This, so much.
And they will likely work on Linux and macOS through Wine, too!