I think exposing the two Win32 window attributes, as two pristine, and separate, X11 properties, is the straightforward thing to do. Trying to define something specific is only making things more complicated.
Regarding the properties names, I think this is not some WM-specific behavior that Wine is implementing, but the opposite. We don't generally implement WM-specific behavior, and I believe we even try very hard not to, so if it were some Gamescope feature that Wine would have to implement I think it would not be acceptable.
However, I think we can consider exposing more Wine internal information to the outside world, in case other tools want to adapt their behavior to Wine. This is not always desirable, and I understand that we may prefer not to, for instance as debugging Wine-aware applications can be more complicated when comparing with native behavior, but in this case I think it can be justified and should be considered.