Recently there was a thing where VAC would erroneously flag AMD’s antilag+ feature as cheating, and issue a ban.
AMD then quickly disabled the feature by default but now Valve also patched detection for it and is now, at least according to these patch notes, reversing the bans.
A VAC ban is only for online games that use VAC, and even then I think they can still use community servers.
It doesn’t lock you out of your account or anything.
Unless they are VAC secured
Even if it’s an entirely different game by a duuferent publisher, you might get premtively banned from playing because the ban is visible on your account.