I am told there is no standard for paint pole threads, but this fits the two paint poles and the broom handle that I have.  This is just a threaded cylinder to use as a starting point for your model.  I am including the .stl file and the .f3d file from Fusion360 so you can add to the model to help with your design.  

edit: 30 March 2025 - adding the .step file as well.

Here are the settings you need to recreate the threads in Fusion 360:
Under "Solid" click on Create, then select Coil. Select a plane, then the 0,0,0 point, 20.0mm is the diameter you want. Then the dialog box comes up:

Change the Type to "Height & Pitch"
Diameter - 20mm
Height - 35mm
Pitch - 5.2mm
Angle - 0.0
Section - Square
Section Position - On Center
Section size 2.00 mm
Operation - New Body
Click OK