After installing the stabilizer, the light blinks when the load is connected
I believe that there is a problem with the connections or the small cross-section of the wires in your wiring.
If we talk about input, then in a normal state of affairs, such strong drawdowns should not be when a load of 2 kW is connected. And they can be either with poor contact of the VLEP wires (or rather branches to the house), also with their small section, well, or the section of the branch to your house. Do you live at the end of the line and far from the substation?
If so, there is nothing to be done about it. Moreover, when you connect the load through the stabilizer, at a lower voltage, the current is consumed even more, respectively, at the input, the drawdowns will be stronger. What were the drawdowns before installing the stabilizer?
With all of the above, I will add that the light may blink due to the speed of the stabilizer. Relay stabilizers are not the fastest, electronic stabilizer (thyristor or triac) is faster.
But I add that when the load is connected, it can blink due to poor wiring, i.e. drawdowns somewhere on twists inside the house, i.e. after stabilizer occur.