I know not every game has a mobile port, and this the way it works for some other media too buying a physical copy of a book doesn't entitle you to an ebook version and vice versa. On the other hand, a steam game can be played on Windows, MacOS, or Linux without restriction provided it's ported or works with Proton.
In any event it still rubs me the wrong way to know I bought Slay the Spire on Steam, and Steam has a mobile presence, and StS has a mobile port, but that still doesn't end with me playing StS on mobile without buying it again.
Hopefully the recent court stuff with Epic and Apple will mean Valve could start putting up their own mobile launcher on iOS, as I imagine they wouldn't see just Android as worth the effort.
Not necessarily true, it's easy to use the tailscale mobile app to create a direct VPN connection to your computer from anywhere, then use sunshine/moonlight for game streaming. However I've never actually tested what the streaming experience is like over cellular data using this method.
Do you even need to do all that? I think Steam remote play works over the internet already, it's just latency and bandwidth is usually unplayably bad anywhere but a LAN.
Maybe steam remote play implements STUN to give you a direct connection to your computer, idk. Sunshine & Moonlight are much better than steam remote play in my experience on LAN though, and are both open source.