Question about linking BNET account to Steam

Hi guys, i’n hoping anyone with good knowledge on how Steam works could answer this question.

I want to play OW2 on Steam and link my Bnet account there but i’m concerned about one thing.

3 years ago, I let my little brother play Modern Warfare Warzone on my PC under my Bnet account (I don’t play it) and he installed cheat program behind my back which led to Activision perma banning my account from playing COD.

I deleted the game, everything and told him to stick to Playstation.

Thankfully, nothing happened to my Overwatch game.

My concern is will Steam VAC ban me and put a red text of shame on my profile if I link my BNET account to play OW2 or is it only Activision games?

I share the same concern;

no as long as you don’t install warzone.
the instance you install and try to run the game on steam you will have a game ban.

Thank you. The install button for COD is all greyed out as it states permanently banned.

I’ll try connect OW sweatly

Did you ever find the answer to this? Worried about the same situation happening even if I do not have an activision account linking to Steam, wondering if a linked bnet account will follow it.