No air gap on a plug-in module. You can certainly try resetting it, but given that the relay does operate from the app it’s just the power’s not provided it’s unlikely that it’s the same issue.
There’s a long-standing issue with GE switches where they will lose the ability to hear Z wave network commands (usually after the end of the warranty period). Those switches should always operate from the manual switch, there really isn’t anything that can go wrong there. But they would no longer work from the app or an automation. That’s the bug where using the airgap to completely reset the switch (or throwing power at the circuit breaker) may help.
Internally, though, a plug-in module like the OP’s pocket socket which will operate the relay from the app but not provide power is more commonly either a burned out component or an overload protection kicking in. And that’s almost always a mechanical fault in the device itself, not a messaging issue like the GE switch can get.
So it may well be worth trying to reset, but if it works, it will likely be for a different reason than why the reset worked on the GE switch. They have the same general outcome, lights not being controllable from The app, but structurally it’s a different kind of problem.