I have several quests from the sanctuary camps - I have to deliver specific items like small energy cells or other items. I have those items in inventory and quest log shows them too, like 2/2. But when I am trying to complete the quest there's no button finish it. Seems like a bug?

You have to go back to the camp and talk to the guy there.

Known bug. Fixed in 1.2.1 which is already on steam.

Ohhh? Does GOG not get the same update schedule?

Feels bad man... Like I legit would have gotten it on Steam instead had I known that.