Outlets only work when you turn on the load on the first outlet

Interfered with the wiring before everything stopped working?

Do the other outlets work properly and fully with the refrigerator running?

There is no such thing that when the refrigerator is working, it seems that there is voltage in the remaining outlets, but when connected it turns out that they do not hold the load?

First of all, you should remove the outlet of the refrigerator and check how and how many wires are connected to it. Maybe this outlet is already faulty, and all the outlets in the apartment from it are connected by a cable. Then there may be a problem with the contact.

There is another version. Do you have grounding? Three wire wiring? UZO or difavtomaty stand? In non-working outlets there is a phase, but there is no zero? This can be checked as follows - you try with an indicator screwdriver - if there is a phase, then measure the voltage between phase and zero with a multimeter. If 0 volts, then there is no zero. After that, check the voltage between the phase and the grounding contact of the socket - if it is, then maybe I'm right.

Then, if in the refrigerator, for some reason, zero and ground are connected, then suppose that your zero has burned out after the outlet of the refrigerator. Then, when the refrigerator plug is inserted into the outlet, zero connects to the ground and the remaining outlets through this contact begin to work. If I’m right, I urgently need to remove it and see what’s in the outlet of the refrigerator, if everything is in order, then look for the distribution boxes and check all the connections in them.

But it is embarrassing that you write that everything starts to work if any device is plugged into this outlet ... Have you stuck devices in a plug that do not have an earthing contact?