Unfortunately this isn’t currently possible. Actions are Godot resources and the inspector doesn’t support selecting more than one row at a time, so you have to copy them individually.
There is an open proposal on Godot’s GitHub asking for something similar (shift+click to batch select properties), and Godot has been adding more copy/paste options in recent dev snapshots, so things do seem to be moving in that direction. Not quite PGM’s Shift+click yet, but a good sign.