This is copied from here.

When using XWayland apps, sudo synaptic or other GUI programs may result in:

    No protocol specified. Unable to init server **: cannot open display: :0.

A workaround for the GUI sudo permissions issue with Wayland is adding to ~/.profile

xhost +si:localuser:root > /dev/null

NOTE: this defeats non-root security advantages of Wayland over X11.