I tried to install the game on another computer - used my save of the new game right before getting 7th companion. Still nothing. I didn't have the faintest idea what caused this, so I decided to reinstall the whole game for the 3rd time.
Deleted everything everywhere regarding PoE II (so everything in AppData and Saved Games folders plus I got rid of the sync file made by steam and deactivated sync), downloaded the whole 45GB+ package, started another new game and got the achievement. Finally.
Based on all this I have to think it might be a problem with Steam synchronization that was bugging my game. The case of installing the game on another computer and it still being broken has to mean either sync problem that the game uploaded to steam server and copied over different platforms, or my savegame files made on first platform were corrupted from the beginning for unknown reasons and synchronization just copied already faulty files.
Thank you for noticing either way, wish I could help more.
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Queeg's post in Recruit all companions achievement was marked as the answer