3 things quickly:
Back to point 6: If, hypothetically, I use a trainer tool on a single player game. Would this be something seen by vanguard and risk a ban? Or will vanguard just whinge crash my LoL/Val game until I close it? Does Vanguard even see this if I don't have Valorant/LoL open?
Does Vanguard run while the LoL client is open or only when a LoL game actually starts?
Does Vanguard run while the Riot Client is running or only during the launch of above Riot games?
If you're using a prohibited third party tool related to League in training mode, there's a good chance you'd still get actioned.
It'll run when the respective clients of the games open, but not Riot Client.exe itself. So, if you are logged in on Riot Client, vgc.exe (which is the actual Vanguard program) launches when you click the Play button for League of Legends and the client pops up, and then closes once you close the client.