Let's see if the problem is DNS or outbound firewall rules.
Please try: nslookup acme-v02.api.letsencrypt.org
If that fails to return an IP, you have a DNS problem.
Stop here and fix the DNS problem before continuing.
If that returns an IP, then try: curl -I acme-v02.api.letsencrypt.org
Does that return:
HTTP/1.1 301 Moved Permanently
Server: nginx
Date: {some date and time}
Content-Type: text/html
Content-Length: 162
Connection: keep-alive
Location: https://acme-v02.api.letsencrypt.org/
If not, then you are having a problem getting to the LE server.
This may be firewall related.
Try accessing any other site to confirm no outbound access.
If that is the case, stop here and update the firewall to allow the Synology the access it needs.
If yes, then I don't understand why the Synology NAS returns such an error.
I would then try updating the Synology to latest firmware.