Is it possible that the night before, he went to the kitchen to take the food and then moved to another room? He might have moved back to the room where his cage is. I would leave the bucket trap down again tonight and also leave his cage on the floor in his cage room - with a ramp up to the cage. Does it have a door that opens at the front? That you can put some kind of ramp up to the open door? If he's cold he will probably have tried to find a warm spot or a cosy spot. I remember someone finding a hamster in a pile of washing or in a jumper in a bedroom.
What is the layout of your house? Stairs? Hallway? Open plan? Have you looked under the sofa?
It might also be that if he's cold he doesn't want to come out. Maybe try leaving the heating on at night tonight, If it's on constant on a thermostat at 18 degrees c, it'll just go on and off when needed.
He'll also stay hidden away if he hears any noise in the house or thinks someone is in the room. The baby monitor is a good idea - some of us have something similar as a "nightcam". Can you view it on your phone while upstairs in bed? Keep positive. It took me two nights to catch Tino

He had been under the sofa the whole time.
I am thinking maybe the kitchen isn't the cosiest place for him to nest and he might have just taken food from there that first night and then gone somewhere more cosy. And yes he may have a hoard. Cucumber would hydrate him for a couple of days but leaving water down is a good idea. In a shallow saucer. In both rooms.
As it's not certain he's in the kitchen now, I would leave all the doors open downstairs at night this time, so he can get back in the kitchen if he's somewhere else and then he might use the bucket trap - if he doesn't go back to his cage.
My sister had a gerbil who escaped once and we found him in a kitchen cupboard! Where he had flipped the lid off a biscuit tin. But gerbils are a bit different and more athletic.