First of all, it is MXP ground, so nobody really can know what they mean
More seriously, as above, a straight "Standby" is clear - no reply, I'm busy. But with further info, as above, I would treat it as needing a reply, and then await them to call back.
Similarly, with say an engine problem on takeoff, I might declare "C/S Pan x 3, Engine Failure, Standby" and I would expect
no or little reply... (but bet I would get one!) not "The weather is this, contact XYZ, how many PoB". But "C/S Pan x 3, Engine Failure, Standby for intentions" I would expect to be acknowledged...
i.e. the Standby refers to a particular item that is being awaited, not a general "keep quiet, I'm busy"
NoD