JvkeOS php_network_getaddresses: getaddrinfo failed: Name or service not known
Your hosting might disallow outbound SMTP by default. Some hosts including DigitalOcean are known to do that. You can usually contact their support to get the port opened.
If that's not it, it's probably still proxy or firewall related.
JvkeOS undefined function proc_open()
JvkeOS proc_open is enabled
It probably isn't. If you have multiple PHP versions installed, make sure it's enabled for the specific version you are using for Flarum.
Your host could also have a specific rule to prevent email outbound that way, similar to SMTP. Check their documentation/support.
Please share details about your hosting if you need further help.