If the freezer is working right your issue is probably not with the “coils”. I’d just keep ice made in some half gallon jugs rotating between freezer and fridge until a tech can check things out.
Also, it could be either the evaporator fan isn’t running or the diffuser duct is clogged with ice. It’s tricky to check for this failure by listening for the fan because it doesn’t run all the time anyway. But see if you can hear it through shut doors (it doesn’t run with doors open), or leave the door(s) open and hold in the switch button usually in the door frame, to keep power to the fan. If after some time you don’t hear the fan, it may have a bad connection or other failure. If the fan does work, check the diffuser duct that may be top center in the fridge back ... it may simply be plugged with ice, so cold freezer air blown toward the fridge by the evaporator fan can’t get into the fridge side.
Be careful if you try chipping ice. You don’t want to scratch the fridge liner. Hairdryer melting can work, if you line the back bottom floor of the fridge with towels to catch the meltwater, etc. But be forewarned - don’t apply too much heat directly on the liner surface; it can warp and cause other issues. Take your time and gently heat/coax the ice plug to melt.
Or, you can always revert to removing all your food to ice chests for a day with the unit entirely off, doors open, and defrost that way, as long as residual water doesn’t refreeze in the diffuser duct when the unit is restarted
Joel