Indeed it's possible, though judging by the release dates, it's not trivial to do right:

- Apple implemented iMessage E2EE sync across devices back in 2011. But be careful not to save your chat keys in iCloud backups (local backups are fine), unless you enable E2EE for iCloud backups as well, which is an option rolled out in 2023.

- WhatsApp appears to have rolled out a form of E2EE device sync in 2023 as well. WhatsApp Web complicates the question of how secure is the E2EE though.