Black is common, yes.
Just gonna copy/paste and edit from the other thread with point to point wiring:
I think you should connect your thermostat adapter wire as follows:
You want to make sure all power is off to both the inside and outside units before unscrewing any wire nuts. Have extra wire nuts of the proper size handy, and wire strippers, in case a wire breaks off in the wire nut when you unscrew it. Also, make sure you have a flat screwdriver small enough to fit into the terminal strip on the wyze adapter.
In your image, you have 2 thermostat wires, one runs to your thermostat, and is using all the wires, and one runs to your outdoor unit and has unused wires. in the below instructions, when I tell you to remove a thermostat wire from the wirenut, I am instructing you to only remove the wire that runs to your thermostat, not the wire that runs to the outdoor unit.
Remove the wire nut from the black wires and insert the C wire from the adapter into the connection and reattach the wire nut ( Note: this is the only case where you are only adding a wire, not removing any from the wire nut ).
Remove the green thermostat wire from the green wire wire nut, and attach the G lead from the adapter to the thick green wire from the fan switch with a wire nut. Attach the green thermostat wire to the G terminal on the adapter and tighten the screw.
Remove the red thermostat wire from the thick red and 2 thin red wires wire nut, and insert the R wire from the adapter into that wire nut with the thick red wire and the thin thermostat wire that comes from the outdoor unit and tighten. Insert the red thermostat wire into the R terminal on the adapter and tighten the screw.
I’m not sure about this, your white wire is Aux, not W1, but it might work. Make sure this is where the wyze app wants you to put the W lead for the common wire adapter
Remove the white thermostat wire from the white heating element wire nut, and attach the W lead from the adapter to the white lead from the heating element and the white wire from the outdoor unit using the wire nut. Insert the white thermostat wire into the W terminal on the adapter and tighten the screw.
Remove the yellow thermostat wire from wire nut leading to the yellow wire from the outdoor unit, and insert the Y wire from the adapter into that wire nut with the outdoor unit wire and tighten. Insert the yellow thermostat wire into the Y terminal on the adapter and tighten the screw.