The heat is predominantly generated in your muscles.
More direct conversion of potential energy to heat is when a person is sliding down a pole to get to a lower floor quickly. With sufficient friction, the descent is at a constant velocity instead of accelerating.
In muscle, some structures slide along each other. Muscle contraction is those structures being made to move relative to each other, using molecular motors that act somewhat like a hand-over-hand method.
As we know, muscles can also extend in a controlled manner. If you are bending down to the ground you allow your muscles to extend while maintaining tension, so that your motion is controlled.
During that controlled extending: potential energy converts to heat in the muscles.
This conversion of potential energy is on top of the baseline heat generation because the muscle is active.
When you stand up your muscles are working against gravity, actively contracting. The energy source for that contraction is, ultimately, the food you have eaten. In the muscles, the conversion of chemical energy is not 100% efficient. A percentage is transformed to actual power output, a percentage becomes heat straightaway.
When you are allowing your muscles to extend in a controlled manner your muscles are active, so some heat is generated just because the muscle is active.
When you are walking downstairs the total heat generated in the muscles is the sum of two contributions: heat that is generated anyway because the muscle is active, and heat generated because the process of a muscle being extended against muscle tension is work being done on the muscle, and that leads to heat generation in the muscle. (That is, that heat is not generated in the muscle when a completely relaxed muscle is extended by an external force.)
In walking we use our leg muscles actively to smooth out the motion; the leg muscles are used actively to provide some level of elastic suspension.
By comparison, kangaroos are known to have Achilles tendons that are optimized to store elastic energy. The jumping form of travelling that kangaroos can do is quite energy-efficient. The power needed for the next jump is mostly from elastic energy stored in the tendon on coming down.
Human walking doesn't have that level of efficiency. Muscle power is used actively both when the centre of mass of the body comes down and when the centre of mass of the body comes back up again. So there is the generation of heat from that power output.