This is one of those errors that crops up, goes away, and crops up again.
The biggest problem with this type of error is that it never fully goes away AND can be aggressive at times which, for me, makes Stadia unusable.
Recreating the problem:
Earlier in Stadia's life, you could minimize your window, maximize the same window and you would receive the error of, "Your mouse is not currently captured by the game". Additionally, you could multi-task (Windows: Atl-tab) to another window, do some work there, then alt-tab back to the Stadia window and immediately receive the error. This would happen in any game where the mouse was necessary to game play.
Possible previous solutions which may/may not have worked to a varying level:
I suspect this error is dependent on the version of Chrome you are using. Some, were just SOLID and this error NEVER happened; didn't matter what you did to try and foul it. Keyboard and Mouse were ALWAYS picked up. Then, a new version of Chrome would deploy and you're right back to this error. Interestingly, I've never once had the window not recognize the keyboard. Never a hesitation or missed keypress. Mouse? I've got a 40% chance of it not seeing the mouse when I come back to the Chrome window.
Can we get a definitive response on what method is employed to attach the mouse to the Chrome instance and when that method is initiated?