and then I tried to paste output to HTTP request body using {{$json.data_object}}, but as result I get my set node inside [Array], how can I paste only content without brackets and “Array”?
What happens if you actually post it? The interface looks like it is trying to be helpful and is telling you it is an array. Are you able to share the data from the image in your first post so I can take a look?
Try using {{JSON.stringify($json.data_object)}} and see if that helps, Without having the data itself to play with it is a bit tricky but that should sort it out for you.