I need to size a motor that aims to turn a worm screw and two gears, to operate two rotating lates (objective deployment and retraction of the two lates at 90 degrees)
Before I even start answering you, I already see two big mistakes in your design and missing information to help you completely
The first thing that doesn't work is to have the same gear for the worm screw and to mesh the second gear.
Indeed, they are not at all (but then not at all) the same tooth profiles.
So to remedy this, you just have to put your worm screw between the two gears. In this case, only the spacing between the two gears is to be changed by the value of the thread bottom diameter of the worm screw.
After you indicated a weight for your slats but what counts in your case is the inertia and not the weight (even if the latter is useful to know the inertia) Indeed the forces relating to the weight are strictly vertical so the weight is not the dominant factor.
Then you have to read between the lines because on your drawing I see the notion of wind. If I'm not wrong and it's windy then the max value of it should be taken into account for the efforts.
Moreover, when you say battens you should have the shape of them (I hope they are not propellers) and the exact size as well as the material to know the mass (useful to know the inertia).
You have to indicate how long it takes you to go from 0 to 90°. All these elements are useful in defining the torque of the motor and the speed at the output of the gearbox.