I don't use VPN so I don't have personal experience and I did not have to struggle with DNS settings. But when I quickly look at your log & resolv configuration in my LE 10 Nightly, at first I would check the /storage/.kodi/userdata/addon_data/service.vpn.manager/update-resolv-conf.sh file, especially line 66 which needs to be modified somehow to fix the syntax error reported above in the log.
I suppose this script should perhaps modify the /run/connman/resolv.conf file, generated by Connection Manager by default, which contains a current DNS server's IP address. So you should update the script to do what is expected.