If I understand it correctly, Bazzite is just a wrapper around Steam and Lutris, so you don't need it ... and I'm not sure you need Lutris either ... so really you could probably just install Steam.
And really you don't even need Steam, what you need is Proton (which is a set of enhancements to WINE that the Steam team made to let it emulate Windows games better). For further info see
this guide or
this (possibly confusing/with outdated bits) wiki guide.