systemd-resolved, resolvconf.service, resolvconf and openresolv. Why, which and how?

I managed to change the script that handles these configuration items in OpenVPN in Ubuntu (tested on 18.04). Here is a patch for that:

--- /etc/openvpn/update-resolv-conf.orig    2019-03-13 19:14:16.163914424 +0400
+++ /etc/openvpn/update-resolv-conf 2019-03-13 19:29:30.380420708 +0400
@@ -15,7 +15,7 @@
 #     foreign_option_3='dhcp-option DOMAIN be.bnc.ch'
 #

-[ -x /sbin/resolvconf ] || exit 0
+[ -x /usr/bin/systemd-resolve ] || exit 0
 [ "$script_type" ] || exit 0
 [ "$dev" ] || exit 0

@@ -43,16 +43,16 @@
        fi
    done
    R=""
-   [ "$SRCHS" ] && R="search $SRCHS
-"
+   for SRCH in $SRCHS ; do
+       R="${R}--set-domain=$SRCH "
+   done
    for NS in $NMSRVRS ; do
-           R="${R}nameserver $NS
-"
+       R="${R}--set-dns=$NS "
    done
-   echo -n "$R" | /sbin/resolvconf -a "${dev}.openvpn"
+   /usr/bin/systemd-resolve -i ${dev} ${R}
    ;;
   down)
-   /sbin/resolvconf -d "${dev}.openvpn"
+   echo "Doing nothing, interface disappears."
    ;;
 esac

You will need to add the following items to your OpenVPN configuration file:

script-security 2
up /etc/openvpn/update-resolv-conf
down /etc/openvpn/update-resolv-conf