right - so its the same issue.
To reiterate - you have in the past installed gnome-shell - and its interfering with Budgie.
In 21.10 GNOME Shell breaks budgie lock screen - upstream (Solus) do not recommend you have both Budgie and GNOME Shell installed. You certainly shouldnt have GDM3 installed - you may have installed this in the past but switched back to lightdm/slickgreeter without uninstalling GDM3
So the workaround is in the thread I linked to - alternatively you can uninstall gnome-shell-common but this will break your GNOME Shell installation.