Does encrypting Time Machine backups require auth on restore?
When Time Machine encrypts a drive, you will have to enter the passphrase to get macOS to decrypt the drive. The drive will mount and all contents are garbled until the key to unscramble the data is provided to the driver that attached the drive to the desktop.

https://support.apple.com/guide/mac-help/choose-a-backup-disk-set-encryption-options-mh11421/mac

iCloud entanglement is for rescuing a user account, not full drive encryption. Your account password can sometimes get a drive decrypted if your keychain contains the secret for a drive.