I tried with a drill bit and its the same issue.
I'm sorry to hear that the testing method did not work out. Thank you for posting the video clips. We have at least eliminated the possibility that it could be your drill bits. Please remember to bring your docket and the drills original packaging to the store.
If you need further assistance, please let us know.
Thanks for the video That basically tells me the chuck is at fault by the same token I will check with two different standard drill bits just to be sure . Also at one stage square shank extenders were available for the use in hand held interchangeable screw driver handles, I am not in my home location where I do have a set and yes it is old.