I think it may have to do with the native resolution of the games themselves. Destiny 2, for example, is rendered by Stadia at 1080p, and then is sent as either a 4K stream, 1080p stream, or 720p stream, depending on the hardware and connection conditions. While it does look better on a 4K TV with a Chromecast Ultra as it can stream at 4K, it is still a 1080p render that is being upscaled.
Games like Red Dead Redemption 2 actually render at 4K natively, so when you are streaming them at less than 4K, or displaying them to something that is 1080p or 1440p, like most computer monitors, maybe that is where the poorer visual quality is coming from?
That is just speculation from me, but I have noticed the same phenomenon you have and that is about all I can explain it with. As for a fix? I don't have one, sorry!