Do you mean that your current VPS has both the control panel and the websites hosted on it?
If so, here's my suggestion:
Set up a temporary VPS and move the websites and email services there first. This way, your current VPS will only be running the control panel.
Next, set up your new VPS and follow the official documentation to migrate the control panel to it.
Once the control panel is fully migrated and working perfectly on the new VPS, you can then move the websites and email from the temporary VPS to the new one.
This approach helps minimize downtime and ensures everything is migrated cleanly.