I think a VAC ban only bans you from that one game, at most from other games with VAC. I got VAC banned in modern warfare 2 10+ years ago, but it hasn’t had an impact on my account/other games. More than a notice on my profile that it happened.
… just to add, the ban was justified. I went into a game and just held down the shoot button with a plethora of cheats on to see what it was like. It took all the fun out of it and cost me a game I liked. Not recommended. : )