The greeter should be set to
agreety --cmd $SHELL, …
which however doesn't work, because
$SHELL is not set at that moment. Unfortunately, that's what you have in https://git.sr.ht/~kennylevinsen/greetd/tree/master/item/config.toml and it really doesn't work. See also https://github.com/openSUSE/openSUSEway/issues/37#issuecomment-806988228 for more.
OMFG, I just wasted about half an hour trying to figure out what the heck is wrong! I thought that I have some problem with PAM.