Exim not listening on external IP for port 587

I think you modified the user:group and the perms because they are wrong.

Here an example with the right perms:

❯ namei -mo /etc/exim4/domains/example.net/passwd
f: /etc/exim4/domains/example.net/passwd
 drwxr-xr-x root        root /
 drwxr-xr-x root        root etc
 drwxr-xr-x root        root exim4
 drwxr-xr-x root        root domains
 lrwxrwxrwx root        root example.net -> /home/test/conf/mail/example.net
   drwxr-xr-x root        root /
   drwxr-xr-x root        root home
   drwxr-xr-x root        root test
   drwxr-xr-x root        root conf
   drwxr-xr-x root        root mail
   drwxrwx--x Debian-exim mail example.net
 -rw-rw---- dovecot     mail passwd