How to fix Apple ID issue correctly?

I’m helping my older parents fix their Apple ID situation. Somehow they have like three Apple IDs and they’re all used for different things. They had an old iMac with their main Apple ID logged in on iCloud. They bought a new iMac and I transferred the old desktop to the new one.

However, in trying to turn on FindMy on the new iMac, I am prompted to sign into an old Apple ID that they no longer have access to. I went through the activation lock process with Apple and I’m waiting to hear back from them. However, I am now reading that the new computer will be wiped following this process. That isn’t the biggest deal since I have backups of it on an external drive using Time Machine. What I’m worried about is that apparently restoring a previous copy of the computer in this way might reenable activation lock and put me in the same situation.

Any ideas or help for the situation? TYIA