Hi KIZ,
I understand how confusing it could be to manage backup between two PC at the same time. First, please refer to the official article: Transfer your files and settings to a new Windows PC - Microsoft Support
Now, it's worth noting that the PC-to-PC transfer happens during the OOBE (Out-of-Box Experience). From your question, I see you mentioned seeing linked devices on the new PC. Is it safe for me to assume that you already finished the setup process and logged in Windows?
If it's correct, I'm sorry but you have to start from scratch again. When you set up a new Windows PC, you'll see a screen offering to restore from another PC. If you've already completed the setup, you won't see this option again unless you reset the new PC.
In short, the Windows Backup app is for your previous PC. On your new PC, you need to be in OOBE for this transfer to work.
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