@Oscarv86 There are a lot of variables that can impact game performance. Let's start by exploring a few of them:
Chromecast doesn't offer any native VPN configuration options. If you wanted to tunnel the Chromecast's traffic then you'd need to configure that somewhere upstream (like your router). Note that a VPN probably wouldn't help in this case, though, since it would add additional hops, latency, and speed decreases to your setup. If your internet connection doesn't work well enough when connected directly to Stadia then I doubt it will work any better with additional constraints.