the effect of the friction is like this:
if the egg is set to spin in a way that its long axis
is tilted a little bit instead of being totally horizontal,
then the contact point will move in a small circle. If
there is friction, the egg will roll and gain angular
momentum along the long axis. since the total angular
momentum is in the vertical direction and conserved (in
an ideal case), the bigger that momentum
becoms the higher the longaxis will tilt, in other words
it will behave like a heavy top or gyro or something like
that.

the 生蛋蛋case is more complicated. if we consider an
extreme situation in that the liquid inside can move
freely, then the torque produced by the friction will
not create much angular momentum along the long axis,
because it only affect the shell,and it's too small a
portion . therefore the long axis will not tilt