

Barrier is only for inputs IIRC. To get Keyboard Mouse and Video (more usually KVM) you need some kind of remote desktop software. Rustdesk is pretty straightforward. I think Gnome handles RDP access natively now if you’re running a Gnome based Linux distro. Otherwise XRDP is a bit of a faff, but solid once it’s working.
In the System settings, under Window Management > Window Behaviour, in the Focus tab, there is a Focus stealing prevention selector. If it’s set to extreme, then it does prevent switching to another desktop when I open a window that gets sent there.
I think that’s what you want but I guess it would mess with all applications, not just Steam. I don’t think you can do it per application.
I remember there being a window management protocol that would allow more control but I don’t think Kwin implements it yet.