For Steam you need steam keys. You can not activate IL2 store keys on steam. Same for IL2 store (steam bought games won't also activate IL2 store games).
As far as I know, it is possible to have BoS bought on both your Steam and IL2 accounts, and have those accounts linked - which is stupid, and just a hack to go around the fact that 777 removed the possibility (which existed before) to have IL2 store bought items also activate the same items on Steam. 777 removed this because people abused it by playing the game from both IL2 launcher and steam at the same time.
I've asked them to keep this possibility for linked accounts (which would allow them to identify either Steam or IL2 launched games as being the same account), but I assume that they haven't got too many requests supporting this, as they simply ignored me.
Even if they sold their items at that time advertising that you can transform IL2 bought items into Steam, and have them activate on both your IL2 and Steam accounts, they just forced my to accept either an IL2 or a Steam key for the pre-ordered products at the time they removed this feature.
I'll never forget how they chose to treat all IL2 legit users as thieves rather than add some little code to force linked accounts remain like that forever once you've activated the Steam keys for IL2 store bought products.