I use “Gnome Tweaks” application to set cursors and they works.
That cursors installs itself under:
/usr/share/icons/Bibata-...
Now when I copy them to (with different name not to be confused)
~/.local/share/icons/
They also works.
But when I copy them to (with different name not to be confused)
/usr/local/share/icons/
they kind of works but not “fully”: they works for example when mouse pointer is over file manager, or Ptyxis terminal, but when mouse pointer is over desktop background, or top Gnome desktop bar, or even Firefox, cursors fall back to default.
I think your problem is more general, and not specific to your installation, and probably not even particular to Silverblue.
I have installed a couple of cursor themes from the repos on a Fedora Workstation VM installation (e.g. oxygen-cursor-themes, bluecurve-cursor-theme, breeze-cursor-theme), and most of them (but not all) have to behavior you’re describing (e.g. mouse pointer moved over desktop background turns it back to the default theme).
The way I understand Linux directories structure / hierarchy is:
/usr/share/
is for system wide functionalities/ features that comes along with system or rpm packages.
/usr/local/share/
is for system wide functionalities/ features that admin can apply/ add - to avoid meddling / breaking what system / rpm provides by default.
~/.local/share/
is for regular user functionalities/ features.
Well, narrowing it down, assuming that this doesn’t happen with another DE’s shipped by Fedora (e.g. KDE edition or Kinoite), and if (preferably) it is reproducible on other distros shipped with GNOME 47, I would say the best place to report it is with GNOME. I couldn’t tell for sure against which project though. Probably Mutter.