It's one of downsides of this technology. There are only few standard resolutions are functioning now and I wouldn't hope to see many updates there now, while more important content needed (shared library for example).
Hello, w1ggspl1tt3r. Same thing for me with my Pixel 3 XL. But I have a question about connecting the Stadia controller to your Pixel 4. Is the rumble (vibration) working when you play on your cell phone with the controller connected to USB-C? Because the rumble never worked on my Pixel 3 XL, neither with a Stadia controller, nor with a Dualshock 4 controller. I even tried with a regular Pixel 3 and a second Stadia controller (courtesy of Google) or another Dualshock 4, but it always gives the same result: you can play it perfectly, but the rumble refuses to work. Even after several discussions with Google Stadia technical support, they still haven't found a solution.
I don't recall rumble feedback while using controller to phone. I made sure it was on but... I probably wouldn't even want it turned on because of battery life for both phone and controller. I know for sure playing via Chromecast ultra there is vibration feedback. I'll try my other games via phone and let you know.