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The structure and color sure do resemble Phytolacca americana, so I think kwanjin is right, it might be something in the same family. The berries seem to be in groups, while the Phytolacca that grows over here has each berry individually attached to the scape. From what I can find, it resembles the seeds of Phytolacca dioica, the Ombu tree. It is a tree in this family native to South America, but cultivated widely as a bonzai and apparently sometimes also as a shade tree.
Thanks ever so much, themoonhowl!
The page you've linked to has a picture of what looks like an exact match. Which means that it's Phytolacca Esculenta.
Pretty surprised to see this plant in the wild in this part of the world (Belarus - Eastern Europe).
Thanks a lot to everybody for being so helpful, I really appreciate this!
What a great forum you've got here!