Have you tried it? I just installed gamescope and launched some games with it via steam launch options. So far I feel like the frame times are better. I use it on top of KDE and with an AMD card. Freesync in Gamescope works too. (Have it allways on in KDE if that matters).
You probably should be using Sunshine/Moonlight instead anyway. The Steam streaming kinda sucks.
I used this for a while, and while it worked great and much better than Steam streaming (never tried it with gamescope tho), the cursor doesn’t appear on Wayland, so I can’t play games using the mouse like EU4.
Which Wayland DE? Have you tried disabling hardware cursor? So for example in Sway/Hyprland or other wlroots based WMs that would be launching it with env:
WLR_NO_HARDWARE_CURSORS=1