OK, it seems it is not possible to have the engine automatically replace the {{{template-parameter}}}
and pass it to the extension parameters.
But, hopefully, the signature of the extension function holds a reference to the Parser object that is more or less the MediaWiki engine.
Then, you can evaluate the content of a variable:
function MyPluginRender( $input, $args, $parser , $frame)
{
$resolved = $parser->recursiveTagParse( $args["template-parameter"], $frame );
var_dump($resolved);
}
HIH