My mental model is that Stadia is just like owning a PS/Xbox, but the hardware is in Google's datacentres.
You pay the one-off cost to buy the console, you then maybe pay for the Pro subscription, but you have to buy your games and those games are locked to that platform - just like with PS/Xbox.
All the other stuff about having games that deliver something unseen before because of "the cloud" are mostly promises and theoretical features at this stage, so I wouldn't bank too much on that.
The games were not re-engineered / ported specifically to run 'in the cloud' as Stadia is attempting. There are some interesting things that could allow, if a developer ever decides to utilize it.