nothing from screen sharing goes off your machine, the only network data from Fazer is trial check and update check https://fazerwm.app/privacy/

I can even explain why screen sharing is required:

if you programmatically move a window so that more than 50% of it overlaps onto an adjacent display the window will be displayed on the adjacent display instead of the desired one, FazerWM uses screen sharing to stream the part that should be visible where you expect it, while the actual window is parked offscreen, also for grabbing thumbnails of windows for Overview and Recent windows features.