Does anyone have any solutions on how the contractor should fix this?

Your contractor should be solving this problem, not you.

You want them to own the problem and be responsible for the fix.

These "new" sliding doors always leak some water when taking a shower. They look cool, but the design just isn't water tight. At least you have a bit of a threshold so you don't get water just flowing out the bottom.

Get used to putting a towel down to catch the water.

I'd pay attention to how the shower is pointing while showering, particularly the handheld part. Can you change the angle of the shower slightly to minimize the problem?

Maybe reset the cap to pitch water back to the pan and cut some slots across the black track to allow water to evacuate.

Add a shower door sweep to the bottom of the doors. Or better yet, have the installer back to add the sweeps and check their effectiveness and also diagnosis the overall issue.

The problem is that the dam (the black metal piece) is inside the sliding door. It should have been outside the sliding door. With its current placement, any water that falls between the dam and the door -- and there may be a lot of it -- will seep under the door and into the hallway.

The doors should have been reversed with the sliding door inside the fixed glass. Then the dam would have been placed outside the sliding door and prevented water from exiting the shower into the hallway.

A shower door bottom seal (example) could be attached to the bottom of the sliding door to prevent water from leaking underneath it. However, the sliding door guide must be wide enough to allow the door and bottom seal to fit (slide) inside. The seal linked above requires a guide with a channel at least 1/2" wide. If your guide were too narrow, it would have to be replaced.

A sort-of solution: Move the dam as close to the sliding door to reduce the amount of water that can fall between the dam and the door.