If you’re going to paint them then it might be worth trying to fill the missing areas and sand. I don’t think you could ever expect to repair this so it can be stained though. Only a new veneer over the entire side could do that and that’ll likely cost you more than a new door.
Hanging a new door is easier than you might think though, especially if it’s pre-hung.
I might check salvage yards and see if you can find doors in your sizes. Most doors can be cut at least an inch or even two off the sides or bottom.