Is it made with Claymation? I have no idea what game it is, but I like the style

Yes Esty, its an an old claymation title. It was developed by a Russian studio, there is a Soviet style to it if that makes any sense. Regretably you can not buy it anymore, but it is considered abandonware I think

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Could it be Agent Gliniarz?

yes! Or Clay Agent for the edition I played. Your turn Kami