That definition doesn't work well because you can have changes in entropy even if no energy is transferred, e.g. by exchanging some other conserved quantity.
The side note is wrong in letter and spirit; turning potential energy into heat is one way for something to be irreversible, but neither of those statements is true.
For example, consider an iron ball being thrown sideways. It hits a pile of sand and stops. The iron ball is not affected structurally, but its kinetic energy is transferred (almost entirely) to heat energy. If the ball is thrown slightly upwards, potential energy increases but the process is still irreversible.
Also, the changes of potential energy in corresponding parts of two Carnot cycles are directionally the same, even if one is ideal (reversible) and one is not (irreversible).
The side note is wrong in letter and spirit; turning potential energy into heat is one way for something to be irreversible, but neither of those statements is true.
For example, consider an iron ball being thrown sideways. It hits a pile of sand and stops. The iron ball is not affected structurally, but its kinetic energy is transferred (almost entirely) to heat energy. If the ball is thrown slightly upwards, potential energy increases but the process is still irreversible.
Also, the changes of potential energy in corresponding parts of two Carnot cycles are directionally the same, even if one is ideal (reversible) and one is not (irreversible).