wpColorPicker: How update colors on input value update?

I was able to solve this by looking into the inner .iris() and check that it has a .('color') method that allows to set a color at runtime.

Thankfully, this .('color') method is supported too by .wpColorPicker(), so one can do:

var new_color = $the_related_field.val();
$the_colorpicker.wpColorpicker('color', new_color);

to overcome the annoyance of not having an update() method.