Other users have reported this with the macOS 27 Golden Gate release, and your backup disks are likely perfectly healthy.
Some users upgrading to macOS 27 Golden Gate have encountered a file system issue where encrypted APFS external drives and Time Machine backup disks fail to accept correct passwords, repeatedly throwing the "disk cannot be unlocked" or "failed to mount" error messages. Because macOS 27 handles secure volume mounting differently, it triggers authentication logic failures across multiple machines—explaining why it's happening on both your iMac and MacBook Air simultaneously.
How to Resolve the Error
Do not erase or format your backup drive. Instead, follow these steps to bypass the bug and safely force the system to mount the disk:
Allow the Hidden File System Check (fsck) to Finish
When an encrypted backup drive is attached after a major system update, macOS often locks the volume to run a background disk check (fsck).
- Connect the backup disk directly to your Mac (avoid USB hubs if possible).
- Open Activity Monitor (via Spotlight or Applications > Utilities).
- Search for fsck in the top-right search bar.
- If fsck_apfs is running, leave the drive plugged in and wait. Unlocking will fail repeatedly until this process naturally completes, which can take several hours depending on the size of your backup history.
More info from Apple: Activity Monitor User Guide for Mac - Apple Support
Run First Aid via macOS Recovery
If fsck is not active but the drive remains locked, repairing the volume container from the boot environment usually resets the mount state:
- Boot into Recovery Mode: Shut down, then press and hold the Power Button until "Loading startup options" appears. Click Options > Continue.
- Open Disk Utility.
- Go to the top menu bar, click View, and select Show All Devices.
- Select your external backup drive, click First Aid in the toolbar, and select Run.
- Once completed successfully, restart your Mac normally and attempt to unlock the drive again
More info: Disk Utility User Guide for Mac - Apple Support