Not enough rudder and the nose will drop in the turn. so you add
rudder to raise the nose and you feel like you are pressed against the
lower side of the plane which is now slipping down hill.


Are you sure?

I think the more bottom rudder you give in a turn, the more the nose
will appear to move lower against a given horizon. All the rudder does
is pull the plane around an axis from ear-to-ear. So if you give too
much bottom rudder, the nose will appear to drop in a turn. If you
give top rudder, you'll have the nose "rise" against the turn.

The classic case of skid is when too much bottom rudder is given, the
nose swings around the ear-to-ear axis, yawing past coordinated turn;
and if the pilot pulls back on the elevator to "raise" the nose back
up, it increases AoA, things could be getting dangerous ...