Water begins to flow when water is poured into the sink.
Dishwasher drain hose raised by a loop above the level of the bottom of the kitchen sink, !!!
Therefore, water when drained into the sewer should not flow into the dishwasher.

The connection point between the drain and the siphon is located below the sewer pipe.
And the dishwasher stinks a lot. All filters are clean. The sewer pipes are clean and water flows easily from the sink into the drain.
What can I check and try?

Most likely this is some kind of malfunction of the dishwasher.