Nope, they are not your iCloud password. Keys for E2E items are kept on device and then there’s a process to join a signing circle for syncing. What this means in practice is to sync you need to allow your new device to be accepted into the circle from an existing device.

https://support.apple.com/en-gb/guide/security/sec0a319b35f/...

The keys are encrypted with your device pass codes. Setting up a new device requires the pass code from another device.