There are ways to synchronize emails between multiple Macs, including the use of iCloud Keychain (to synchronize passwords), but if you want to also be able to synchronize the email CONTENT, that happens automatically when your email is IMAP or MS-Exchange, as all such emails are stored on the server and download automatically on other devices. However if you store email locally (not on the company's servers), or use POP email, or don't or won't use iCloud Keychain to synchronize passwords, synchronizing between Macs is possible but does require some "technical" steps of copying certain folders and files over, some of which are not normally visible to the user.
The simplest way for "disaster recovery" (which is what you are interested in, it sounds like), is to keep one or two Time Machine backups of your main computer current. If that computer fails, you can use Migration Assistant to "migrate" everything from the main computer user account(s) to another device. Then that other device will have all your files and accounts just as they are on the main computer -- all emails, passwords, settings, files, everything. You can also do this even if there has not been a disaster.
The Apple supported method of keeping things synchronized between Apple devices is to use iCloud for that. It can keep files, emails, etc. identical between multiple Apple devices.