https://help.steampowered.com/en/faqs/view/571A-97DA-70E9-FF...
> Q: Can I use bans in other games to block users from playing in my game?
> A: No. VAC and Game bans should only prevent the user from playing on VAC secured servers in the game they received a ban in. A permanent ban should only be issued for your game if the user was caught cheating in your game.
https://partner.steamgames.com/doc/webapi/ICheatReportingSer...
It's complicated. Valve has conflicting guidance on this. What is Valve's actual position? The 13 year olds who cheat also buy IAP. In their opinion, if there are a lot of cheaters, sell pay to win items.
Otherwise, the consensus is hellbanning, meaning putting all the cheaters together in a server, and VAC queries are used to achieve that.