Steam (Windows): no space / where is Steam installed?

I’m trying to install No Man’s Sky ( using the Steam (Windows) installer.
I successfully installs Steam (although there are some error messages popping up but they seem inconsequential). I manage to log in, and then there’s the Steam’s installation screen where you see how much space it will take on disk: about 9GB. However when I press ok it says that I have no space on the device.

Just before trying the install, I went to lutris settings to change the default game installation folder to /mnt/media/games because my $HOME is almost full. But I don’t find any wine stuff or steam installation or anything in /mnt/media/games, so I suspect it must have tried to install the windows steam in my $HOME somewhere?
In that case, how can I change the location to install it?

Steam manages the games on its own; all Steam games are installed within Steam folders, Lutris has no control over it (when it does it offers you a dialog to choose/confirm location during install).

Winesteam prefixes (32/64 bit) can be found in the runner settings (default location should be in ~/.local/share/lutris/runners/winesteam).

If you want to change it, you can run Winecfg for the prefix (in Lutris it’s available in menu for any game of the runner), and then link any folder in any location as a virtual Wine partition; then run the Steam interface, add Steam gamesfolder to that partition in settings, and set it as default (or pick it on every game install). I think Steam also allows moving installed games between gamesfolders without reinstalling.

Though, to be honest, games that don’t require much fiddling (which often can be checked here) are more convenient to have installed with Proton (in the native Steam; you can install it same way as a native Steam game and then import into Lutris, or use the Steam install script… which isn’t hard to make in these cases if it’s not made yet).