Awesome, thanks in advance for your efforts.
Got around to testing, and as my post now says, it seems to be a bug with gamescope or steam’s game ui.
In the meantime, running it from desktop mode with gamescope -w 568 -h 320 -fine -- %command% as your launch parameters for the game [if running from steam] should provide a great experience, just make sure you have the game’s graphics set to fit and 1x as those parameters let gamescope take care of scaling.
If not running from steam, your launch command would be gamescope -w 568 -h 320 -fin -- ./CrossCode