Scaling an electrical motor to open my door knob
Your motor can pull 800g, or 8N with a radius 1cm pulley, but you used a 5cm (diam 10cm) one, which means you are down to 1/5 of that value, being 8/5N.
By using the pulley scheme that you are, the needed force is halved to 13/2N, much more than the available force.

You can either trim down the winch to about 1cm, or apply more tiers of pulleys (yet with every pulley you also add drag, so have some force extra...).

With your current pulley diameter you would need a 5-tier pulley system, so i would advocate the smaller winch. (possibly just use the motor axle, it will take more turns to winch in 10cm of wire, but it will turn more quickly if its not as near to its operational limits)