Your issue is related to this problem in the glibc Galaxy API.
Currently steam deck users don't have an intuitive fix for it due to the necessary tools not being present on the proprierary steamos Linux distribution.
While others have found success overhauling their installations from native Linux to an emulated windows install with Proton, doing so disables steams cloud save option and would require migrating all of ones mods from the Linux format to the windows format.
If you'd rather not go to lengths, you can restart your steam deck into the last stable build by restarting it and holding the ". . ." Button on the right lower side. Then select the option for previous build, it should be the second one after "current..."
Your steam deck will then display some scrolling text and will eventually boot into the big picture mode. Co op will then work. You will need to do this again if your deck automatically updates on you if you want to play sdv coop until steamos releases a new build to address the glibc issue or someone finds a series of commands steam deck users can use.
