Can I export an SVG animation?
Animator does use SVG animations, but it doesn’t export/produce a vanilla.svg file.
Animator uses SVG internally to render what you see in the browser. SVG by itself is not enough to render the animations or interactions that you create in Animator (we have to augment with HTML + JS + CSS) so "vanilla SVG" isn't a possibility.
Why doesn't Animator support this feature?
The driving mission of Animator is for building interactive animations and UIs; exporting to vanilla SVG would require removing all interactivity, which would be a step in the wrong direction per that mission.
What if I need to export a static SVG?
If you're looking for static vanilla (still) SVG, you should be able to export stills from your vector design tool.