Time Machine Backup Failure on M2 MacBook Air

The part that concerns me is that Disk Utility can’t mount the backup disk at the device level and Migration Assistant has stalled twice.

Since you can still browse the backup, I’d copy any irreplaceable files from it to another drive before doing any more repair or erase attempts.

You also don’t need the macOS versions to match exactly for Migration Assistant. Apple says the Mac should be up to date, but matching versions aren’t required.

Time Machine isn’t a bootable clone. It backs up your files, apps, accounts, and settings, but not macOS itself.

The /nix folder is a special case. Nix on modern macOS commonly creates a separate APFS volume mounted at /nix, so I wouldn’t assume that volume was included in your Time Machine backup. You may need to reinstall Nix and restore your configuration/project files separately.

A copy of your home folder is definitely worth keeping in addition to Time Machine. Time Machine gives you more than that, including previous versions and other migratable data, but I wouldn’t rely on any single backup.

Given the mount error, I’d preserve what you can access first, then work on the Time Machine disk itself. Apple’s current troubleshooting also recommends repairing the backup disk with Disk Utility and trying another backup disk if it can’t be restored reliably.

Time Machine is not a complete disk clone. 

Apple states that Time Machine backs up your files, but excludes system files and apps that are installed as part of macOS. 

When macOS needs to be reinstalled, Apple recommends reinstalling macOS and then using Migration Assistant to transfer your information from the Time Machine backup. (Apple Support)

Time Machine can nevertheless restore your personal files, applications, user account and settings through Migration Assistant.

It also provides something a simple copy of your home folder does not: access to previous versions of files and files that were subsequently deleted. (Apple Support)

Regarding your Nix installation, I would not assume that it should be present or absent. 

Time Machine can exclude files and folders, and Nix may have files outside your home directory. 

The safest approach is to check the backup for the particular Nix files you need. Your separate copy of your home folder is therefore an important additional backup.

Your two failed Migration Assistant attempts are worth investigating. 

Four hours at "8 minutes remaining" does not by itself establish that Migration Assistant has failed, but repeating the same behaviour twice makes it reasonable not to keep repeating the same procedure.

The -69842 result also should not be interpreted by itself as proof that the Time Machine backup is damaged. 

Since you can access files on the backup, I would preserve the backup and not erase or reformat it while you are still relying on it.

The fact that you used the same macOS version, 15.7.5, is fine, but Apple specifically says that the Macs do not have to be running exactly the same macOS version for Migration Assistant. (Apple Support)

If Migration Assistant continues to fail, a reasonable fallback is to reinstall macOS on the repaired Mac, then restore your personal files from your separate home-folder copy and reinstall applications manually, while continuing to keep the Time Machine disk intact. 

You can also use Time Machine directly to recover individual files or earlier versions. (Apple Support)

Apple's relevant documentation is here:

Restore your Mac from a backup

Transfer your information to Mac with Migration Assistant

Exclude files from a Time Machine backup

Back up your files with Time Machine

Restore items backed up with Time Machine

The next useful step would be to look specifically at the exact Disk Utility message containing -69842. 

That would let us distinguish what Apple documents from what we can reasonably infer about your particular backup.