I’ve ahd similar problems with fridges.
The problem is simple.
The “cold” comes rom a bunch of freezer coils, usually between the freezer above and the chilled area below. The thermostat turning the fans on blows enough cold air from the coils into each compartment to maintain the desired temperature.
Hence, any frost condensation happens on these hidden coils, not in the freezer compartment.
There’s a timer - mechanical round thing like a hockey puck on the back of older fridges, electronic timer on newer fridges. (Down where the compressor and all the other mechanical crap is).
Every few days it tells the coils to heat instead. This melts accumulated frost off the fridge.
There’s a thin plastic pipe, that lets the accumulate frost when melting drain off down the back of the fridge into a flat wide pan under the fridge.
Here’s what can go wrong:
Timer dies; I’ve seen this on several fridges.
If it dies stuck in the melt cycle, your fridge actually becomes quite hot inside. I’ve seen this once or twice with friends’ fridges.
If it dies in cool, then you never defrost the cooling coils, they fill up with ice, and the fridge gradually becomes more ineffective. It’s cooling, but the ice blocks the airflow over the cooling coils, so no cold air circulates the fridge.
(I used to have to unscrew the bottom plate of the freezer compartment, lift out the metal plae and the Styrofoam piece, and use a hair dryer to melt the ice; then it was good for a week or two depending on humidity. Finally I replaced the timer - that’s actually quite cheap.)
Yours is a different problem I’ve had once, too.
the fans blow air through the cold compartments. they also pick up fluffy bits and blow them into the cooling coils. In my case, it was bits of onion skin; sometimes it’s wet dust bunnies. Sooner or later, these bits will clog the drain, so when the melt cycle comes along, the water cannot drain into the bottom pan. Then, it freezes again (except for an overflow that runs down inside the fridge.)
A wad of frozen ice is much less effective at cooling than lots of metal fins, so once the coils are iced over, the cooling effect is much less. This is what you see.
the solution is simple. For short term relief, find where the little plastic pipe comes out the back of the fridge. Pull it off (most fridges, it is pushed onto the drain hole stem) and clean the hole with a pipe cleaner or similar thin tool. In some fridges, you see the drain plastic pipe come first into the cooling compartment, then through the back. If the debris is too big to bell cleared with a pipe-cleaner, it will eventually clog the drain again. you need to unscrew the bottom plate, access the drain area of the cooling coil, and get rid of any clogging dirt and debris.
(If the problem was just plugged hole with no ice buildup you’d have a normal fridge but lots of water draining into the bottom of it. Since you also see ineffective cooling, the coils are drowning in ice also. )
You can probably watch your repair guy do exactly this.