Have you set the new network informations also in your system network configuration? Add it or change it at the hestia backend isnt enough - the dig shows that you dont have any internet.
So, what’s in your exim mainlog? Is exim up and running? Can you manualy send a mail over telnet (google it) to validate the receiving process? For sending, basicly the same - mostly “check the log”.
Not gonna chat debug that one with you: its not clear who us the sender or receiver, not clear what you try to send to who and so on. Also not if you send it to the same server and a few more points.
Please explain exactly what you’re testing, what you expect to work and what you’ve aready tested and changed to the system