Bummer deal. A door should stop rain. There are quite a few buildings with doors.

If they all leaked, we'd have a problem. Some doors are just junk, but your door looks dang familiar. If it is the brand I'm thinking, I have a number of those doors. They seem to do fairly well.
Get out a hose and start spraying. Start at the lowest point. The first pic makes it appear that the water is coming under the threshold, but time after the rain changes the look as water dissipates. The hose spray will highlight the leaking with a better view of the flow.
I'm not sure where it was caulked underneath, but look for leaks on the threshold extension and also the joint between the threshold and adjustable sill. The corner gasket in one picture looks a little beat up. Those are rarely the sole source of leaking, but maybe you'll get lucky.
I did like your idea with the sweep. That was a good step. Too bad it didn't fix the leaking. I'd also caution against adjusting the sill too tight. It actually kinks the sweep brush/squeege and causes premature wear. It also makes the door harder to operate. They work best with goldilocks adjustment.
Good luck. I'm guessing you will find the source.