I have moved into a house where someone with an electric wheelchair lived, and most of the doors and frames are damaged. Can you just fill them with some special filler and then paint them? The worst part is how to repair the frames, as there are large wood chips missing in some areas.
In many cases, it can be easier and cheaper to replace the frames. They are not so expensive. Otherwise, if there is extensive damage, you can fill with two-component filler, regular quick filler does not work so well if the damage is deep. There are many kinds, I have bought from Biltema myself.
Wood putty should be used as it becomes harder and is suitable for your purposes. Unfortunately, it is a hassle to sand but holds well. Common wall filler is said to shrink.
Plastic Padding works well! It's also easy to sand...