That is the case with this inexpensive unit. It just doesn't draw any power when the plug is pulled out... Standby, however, requires almost no power, so from my point of view it's not a problem.

It depends on what you mean by standby. The corresponding small orange indicator will always light up (the indicator display goes out).
In operation it lights up brightly, in standby it becomes darker (but still lights up). The change from operation to standby is accompanied by the switching of the relay (distinct clicking sound).
The unit does not have a mains switch to disconnect it from the mains, but the plug has to be pulled out. However, this is "normal" for this type of appliance (e.g. TV), because otherwise it cannot be switched on again with the remote control.
Therefore, in my opinion, there is no defect here, unless the display always remains on.

Looks like a defect. Mine switches off completely!