Any idea why farmer don't give carrots to villagers in chamber ?
They don't have enough carrots yet.
I prefer the Breeder / Iron Farm combo. The villagers are more able to interact, so they start sharing food earlier.
I use a 9x9 garden with a waterlogged iron trap door in the center. Iron, because it can't be opened accidentally. At one end I build a 5x9 platform for beds and a drop opening.
The zombie is in an alcove that is closed at night with a block and sticky piston, powered by an inverted daylight detector.
The roof then becomes the 9x15 Golem spawn area (9x14 plus the end wall). This feeds into a lava pool above a layer of hoppers.
No, it's not the fastest breeder or iron farm, but it's quite adequate. If I want to stop the breeding, I remove 4 of the beds. If I want to stop the Iron farm, I switch the piston to always on.