After some pretty quick updates following the initial release of Steam Play, things have quietened down somewhat. However, work on the next version of Steam Play is in progress.
It was expected it would slow down after the initial release period, since they were rapidly pushing out fixes to get it into a somewhat stable state. Stable enough for them to put it into the main Steam client that is, since you no longer need to opt into any beta to access Steam Play.
Going over some recent changes: DXVK 0.72 has already be pulled in, along with a small fix for .NET launchers failing. The update to DXVK by itself is a pretty big deal, considering the amount of fixes and improvements that make it into each release. Steam Play's Proton is currently on DXVK 0.70 which is three versions behind now.
Looking at the custom build of Wine they're using, there's a good few windowing issues being fixed including issues with multiple monitors, a workaround for black screens on alt+tab (a bug in mutter) and better ALT+F4 handling for the GNOME Shell desktop.
No idea when the next version will come, since Valve haven't given out any sort of roadmap for it. You can see any info across Valve's various GitHub repositories.