By background color, do you mean the white field — the “page” color? That’s not a theme color, it’s controlled by Inkscape. And in fact, for reasons I’ve never understood, it’s a document property, so it’s set per file.
If you go into File > Document Properties… the Page tab has a Background section where you can change the color and/or turn on checkerboard transparency. But it’ll only take effect for the current file.