Valorant will not work because of the anti cheat. See https://areweanticheatyet.com/?search=valorant&sortOrder=&sortBy=
For Minecraft you can install Prism Launcher with Discover in Desktop Mode. Just add it to Steam afterwards.
In general there are several ways to install non-Steam games. I usually use Lutris to manage them. You can also use Heroic, Bottles or just add the game’s exe to Steam and configure it in Steam to launch with Proton.
The patch needs 130 GB of free space, maybe you don’t have enough and it gets into an error. I would uninstall and reinstall the game. Your saves and settings should be untouched by that.