In the case of Linux there are an even larger number of widget sets: see
On the graphics side, though: classically, it's been XWindow: a base library called XLib talks the X protocol and does lower level manipulation; widgets implemented on top of that. With XLib you do things like repaint a window in response to expose events, somewhat analogously to a WndProc getting events.
Wayland has its own libraries.
Then you have things like working with framebuffers and SDL and whatnot.
However...
> This would make vendors write more gui software for Linux
What makes you think vendors want the native look and feel?
Even on Windows, there's a long history of apps wanting to feel "unique". That's what they want: full customization to fit their branding.
I started a war answering there. You want a monolithic standard api? Great you do it.
You know what you'll get? Even more options.