Splitting the two during a migration.
WHEN THIS APPLIES
You want the website on a new server and mail unchanged, at least for now.
Sensible, because mail migration is the harder half.
WHAT TO CHANGE
Only the A records for the domain and www, to the new server.
WHAT NOT TO CHANGE
MX records The A record for the mail hostname SPF and DKIM records
THE CRITICAL SETTING
On the new server, cPanel's email routing for that domain must be set to remote.
If it stays local, the new server delivers mail for your domain to a local mailbox instead of sending it to where mail actually lives.
The sender sees no error and the message never arrives.
That is the failure people cannot explain, and it happens on almost every partial migration.
TESTING
Send from the new server's contact form to an address on your domain. Confirm it arrives at your real mailbox.
That single test catches it.
MOVING MAIL LATER
When you do, change the MX records and the mail hostname, and set routing back to local.
Download mailbox contents first.