I’m logging on remotely to a router (RB4011), the engineers are not available to tell me if the router is powered via POE, AC adapter, or both.
Is it possible to get this piece of information from any of the functions accessible via Winbox/Web interface?
No.
Actually, the answer is maybe.
With the factory ac adapter, it makes 24v.
So under system/health the voltage would say 24.x V.
If your POE is a 48v model, under system/health the voltage would show the higher voltage.
But if the POE is of the 24v standard, then I dont think you can.
Routeros seems to report the higher input voltage.
The way mikrotik devices (most of them, some need explicitly distinct voltage levels for supporting diverse PoE out options) combine different power sources is pretty simple: they are all fed via simple diodes and then joined together. Diodes prevent power from leaking out. That also explains the fact that RB device always runs off the power supply with highest voltage. Also explains slight voltage drop (diodes usually drop voltage by around 0.5V). And also explains why it’s not possible to pinpoint exact power source used unless they all provide different voltages.
In OP’s case this means remote engineers can simply disconnect the barell plug and if PoE in source actually provides power, RB will continue to work. Same thing with PoE in powering (but that connection might be needed for data flows so it might not be possible to disconnect it).