Whirlpool Refrigerator Still Cold, But Barely

Brand: Whirlpool
Model Number: WRS571CIDM01
Main Symptom: Water dispenser not working, fridge and freezer cold but weak
What happens & when:

Hi! Yesterday morning we discovered the external water dispenser on our fridge wasn’t working. The ice dispenser still dispensed ice.

In the evening, we found the ice melting and the items in the freezer getting soft. We tried turning it off and on. The evaporator fan is still working and the fridge is cold. The ice in the freezer is still melting. It seems like it’s barely holding on.

This is a last ditch effort to see if there’s an easy fix before we order a new machine. Thank you!

If you pull off the freezer’s back panel, does the evaporator have a nice light frost coating across the whole coil? Also, if you disconnect the 5/16” water tube at the bottom of the door and aim the tube that is coming from the back of the appliance into a cup or bowl, then press the dispenser — does water come out and fill it?