@SilverOwly Does the lag only happen when you play Stadia games? Or is it also the case when you play other games?
In any cases, this would be a good feedback for the Google team. You can submit feedback straight from the Stadia app.
This is expected behavior for most bluetooth earphones, bluetooth just has a lot of latency no matter how you cut it. Some are better than others, but it is a wireless protocol to be avoided for gaming or even just watching movies most of the time. There is a reason you'll never find a wireless gaming headset that relies on bluetooth.
You may be able to get a bluetooth headset/headphone that supports APT-X Low Latency which helps in this regard but both devices need to support this. I assume your pixel should support this protocol.
Taking Stadia completely out of the equation, what's the experience like watching a YouTube video with those same Bluetooth headphones? Any change if you also connect the Bluetooth game controller? How about if you switch the phone from WiFi to mobile data?
It is normal to have a bit of audio latency between the device and Bluetooth headphones but I don't think that should impact the video stream - unless, like you said, there's some WiFi interference going on.
This is a mysterious issue, where bluetooth earphones causes wifi to drop to unplayale rates. And yet sometimes not at all.
I tested speedtest, wifi can be all good with and without bluetooth earphones + gamepad.
Then all of a sudden. For no appearant reason, on my pixel 2xl, my jbl bluetooth earphones causes wifi speed to cut in half and and stability completely gone, the moment I open my jbl bluetooth earphones and the moment I close it, wifi works completely fine again.
Yet sometimes it works perfectly with and without. And then while playing, for no appearant reason at all, all starts lagging due to the bluetooth, and instantly no lag again when I disable bluetooth.
This happens with me consistently as well, and only with Stadia games. I have a Pixel 4 XL and when I try to play Stadia on my Chromecast Ultra or my Phone, my pixelbuds (or Bluetooth keyboard) break it how the OP described. When I turn off Bluetooth on my phone the problem goes away. @Ivan