Parse Dashboard gets the Parse Server version via the serverInfo endpoint providing the masterKey, for example:
http://example.com/parse/serverInfo
To generate the response for that endpoint, Parse Server gets the version directly from package.json via:
import { version } from '../../package.json';
So I don’t believe that the version is exposed as a property of the Parse Server instance. But it seems a good idea. Please feel free to open a feature request.