I suspect you may be having the same issue as me: Framework Laptop 13 locking up on Fedora 42 with Wayland+GNOME
I tried switching to KDE Plasma, and it seemed to work, although personally I hate the look/feel of KDE. Today I’ve been trying GNOME-on-X11 instead of GNOME-on-Wayland and I haven’t experienced hangs so far. I’d try GNOME-on-X11 first before trying KDE Plasma if I were you: you should be able to switch at the login screen by clicking the little gear icon in the bottom right of the screen once you select your login user.
Update: I’ve been using GNOME-on-X11 for many hours today and it hasn’t crashed or hung once, so this definitely seems to be specific to GNOME-on-Wayland. Other DEs that use Wayland work, so it’s some interaction between GNOME and Wayland specifically, possibly due to updated AMD drivers.
The downside of GNOME-on-X11 is that they haven’t implemented touch gestures for most things, so it’s not a great downgrade, but it does at least not crash or hang.