Is there a 3D format which is a 3D extension to SVG?

No, there is no such standard extension to SVG as part of the W3C.

The closest that exists is the W3C Community Group, "Declarative 3D for the Web Architecture Community Group".

Editorial: nor should there be. While SVG is great and vector, it is a presentation format, not a data-interchange format as you seek for 3D. For example, the painter's model of SVG describes the visual layering of elements, a concept that is unrelated to the vector data. Similarly is the presentation markup on fill and stroke color/opacity, instead of metadata such as material. Though it's not a great format IMHO, you should look at COLLADA if you want an XML-based file format for 3D data.

If the W3C feature of SVG is critical, I don't know of anything. And if you want to make an SVG graphic into 3D by changing some outer tags and leaving the rest alone, I don't know of anything either.

But if what you like about SVG is that it is a declarative language for 2D graphics that can be rendered in a browser, and furthermore that the objects are "persistent" in the sense that you can change an attribute in the DOM and that change is reflected in the browser (in contrast to a canvas approach where making a change means redrawing the picture), then X3D is a candidate. They appear to have liaison and cooperation agreements with W3C etc. Javascript libraries support rendering in a browser; see demos at X3dom, Cobweb.