Doorknob sticks if door closes hard
It could be that the small half cylinder on the bolt is getting into the hole in the striker plate and jamming. This would mean that the striker plate is set too far out in the jamb.

It will be a pain to relocate the striker plate in a little, but you might have to do it. To test this, examine the movement of the small half cylinder as you close the door. You could use a felt marker to put a mark on the end of the half cylinder. The mark should stay visible as the bolt goes into the striker plate.

You could place a thin shim in the doorstop opposite the lock or two shims one above and one below and see if this stops the jamming when you close the door hard. If this stops the jamming you could just leave them in and use it that way

EDIT

If, due to the peculiarities of your door, you can't get the striker plate adjusted, you might consider going to a non-locking handle. The non-locking handles have a plastic bearing strip on the side of the bolt so that jamming would not be possible. You would then install a dead bolt lock requiring a key on the garage side.

One problem with the locking door handle on an exterior door is that it is easy to get locked out. After one or two episodes over 20 years we changed to a non-locking door handle and a deadbolt lock (which requires a key for locking) on both the front door and the door into the garage. Some neighbors have given us a key to their house and have had numerous lockouts (front door or rear French doors) in which they come to us for the key. Another neighbor also gave us a key for the same reason.

EDIT

Another possibility is to replace all or part of the weather stripping with some which is stiffer than the present one so that the door is stopped before it goes in far enough to allow the small bolt to enter the striker hole.