Regular hard plastic handles and knobs never suffer this problem but soft-touch, cool-touch or other coatings intended to up-market an appliance based on polyurathane can develop the sticky surface.

This happens to all sorts of things and I have had two pairs of new shoes with soles of that material in storage for a time only to find the soles had turned into something resembling chewing gum when I needed them.
I recently bought a quality DAB radio only to find the knobs are going the same way and the waterproof coating of tents and raincoats are similarly a nuisance.

The manufacturer of my tent recommends rubbing talcum powder into the surface to prevent the stickiness being a problem. This seems to work quite adequately, though Fuller's Earth might be better.

The alternative is to replace the knobs and handles if they are available. I suggest a very strong letter to the manufacturer complaining about the inferior materials they use on an appliance intended to last a decade or more.

What you are feeling is residue from the manufacturing process. You should wash it with Dawn. Be careful not to get the electronic parts wet.