This scirpt is ran by the systemd service.
In Fedora the service has priviledges dropped to the mysql user.
Thus "chown 0" will always fail

Never parse 'ls' output!
http://mywiki.wooledge.org/BashFAQ/087

diff -Nau mariadb-10.5.0/scripts/mysql_install_db.sh.old mariadb-10.5.0/scripts/mysql_install_db.sh
--- mariadb-10.5.0/scripts/mysql_install_db.sh.old	2020-09-08 15:20:02.075081944 +0200
+++ mariadb-10.5.0/scripts/mysql_install_db.sh	2020-09-08 15:21:36.251043330 +0200
@@ -490,13 +490,16 @@
   fi
   if test -z "$srcdir"
   then
-    chown 0 "$pamtooldir/auth_pam_tool_dir/auth_pam_tool" && \
-    chmod 04755 "$pamtooldir/auth_pam_tool_dir/auth_pam_tool"
-    if test $? -ne 0
+    if [ `stat "$pamtooldir/auth_pam_tool_dir/auth_pam_tool" -c %u` -ne 0 ]
     then
-        echo "Couldn't set an owner to '$pamtooldir/auth_pam_tool_dir/auth_pam_tool'."
-        echo " It must be root, the PAM authentication plugin doesn't work otherwise.."
-        echo
+        chown 0 "$pamtooldir/auth_pam_tool_dir/auth_pam_tool" && \
+        chmod 04755 "$pamtooldir/auth_pam_tool_dir/auth_pam_tool"
+        if test $? -ne 0
+        then
+            echo "Couldn't set an owner to '$pamtooldir/auth_pam_tool_dir/auth_pam_tool'."
+            echo " It must be root, the PAM authentication plugin doesn't work otherwise.."
+            echo
+        fi
     fi
   fi
   args="$args --user=$user"