12VDC,3.8A On-Board Power Supply
the relay module you have chosen contains an inbuilt amplifier, a small current (less than 3mA) into the signal terminal is all that is required  to turn the relay on.
the module will the draw 100mA from the 3V terminal to operate the relay. 

So your power supply will need to provide 100mA, but your Micro-controller only needs to source 3mA from its output pin 

Datasheet page 9 shows the amplifier circuit comprised of a MMBT2222 transitor and a few resistors.

Whether it's 100mA when on or when off is entirely your choice, the relay has 3 output terminals and which you connect to your circuit  will determine if the relasy needs the signal and consumes power to act like a conductor to act like a insulator.

your controller board can supply 300mA at 3.3V so some of that can be used to power the relay module (3.3V is close enough to 3V to not cause any problems for the relay)

the relay is not a power supply it's an electrically operated switch. you'll need to provdee an AC supply between 80V and 264V to run the meanwell power supply module and the have the relay output in series with one of the AC wires.

You haven't said where your 5V is coming from... but if it's produced from an AC supply the same Ac supply can be wired to the relay output and the meanwell module.