You should read documentation (wiki) and make your own backups if you don't have the right version (Network Edition or OpenSource Edition + ZeXtras).

Using one IP per domain and setting up zimbraVirtualIPAddress per domain.

Download last version from their website, un-archive it and launch "./install.sh all".

I think SNI only works for https, not imaps/pop3s/smtp.

Looks like the LDAP database is in bad shape, you should restore a backup/dump.

Confirmed on CentOS6 and Ubuntu 18.05 (with last 8.8.15-P20).

Did you upgrade to the NG modules?

If you did, the CLI changed.
https://wiki.zimbra.com/wiki/Zimbra_NG_ ... dmin_Guide

with regard to the RAM memory, the old server has 128 Go while the new one is only 32Go of which 24 allocated to WM. This might be the issue. If Zimbra was installed with 128 GB of RAM available, the installation script tuned both mysql and the Java Virtual Machine for 128 GB of RAM. Now there's on...

Same amount of RAM than previous server?

As Vavai suggested, you should look in /opt/zimbra/log/mailbox.log (and maybe /opt/zimbra/log/zmmailboxd.out) for errors.

How much CPU and RAM on the new VM?