Greeters like phrog want to store runtime data there (e.g. dconf data in
.config) so the _greetd users's home directory should be writable.

Cheers,
 -- Guido

Quack,

I'm not familiar with how phrog works but _greetd's home directory is
owned by itself.
On my system I'm using wlgreet and I can see mesa left some cache files
in it and the permissions are right.
What permission do you have on yours?

Regards.
\_o<