MLX90614 breakout board dead
The sensors appear to be pretty simple to hook up.  I don't see a lot of room for getting things wrong in the example circuits.
What I do notice is that the GY-906 DAA is in a metal can housing, and that the AliExpress modules show the housing sitting flush on the PCB.
Since the traces are also on that side, I'd take a look and see in the housing has cut into the solder stop over the traces.  That could easily cause a short circuit between the Vin and ground connections.
If the housing is shorting the traces, then you could use a soldering iron to melt the solder pin by pin.  For each pin, use a small screwdriver to lever the sensor up a little bit.  Melt solder, lever up the sensor by that pin, hold in position, remove heat, let cool, go to the next pin.  You don't need much clearance to fix the short.
It is also possible that the pins are shorted to the housing underneath.  In that case, you'll have to completely remove the sensor from the board.  Repeat the above procedure until the sensor pops out, then clean the solder from all the holes and the pins.  Solder the sensor back in place.  Don't flood things in solder, and make sure to pay attention to where the tab is.

The above assumes that there's a functional sensor on the board.  Keep in mind that it is entirely possible that there are factory rejects or otherwise defective parts on the boards.