Wasted money on Windows Licenses

Retail keys can move between PCs, so your money is not wasted. What you describe fits the most common cause: a key only activates the edition it was bought for. A Home key will not activate a Pro install, and a Pro key will not activate a Home install, even if the key is valid. After your wipe, each PC got the wrong edition for the key you are entering, so the troubleshooter reports no linked device and cannot activate. How to fix it, in order:

• Check which edition each PC is running. Settings > System > About shows Windows edition, or run slmgr /dli in a terminal. If the AMD PC has Pro installed and you are entering the Home key (or the other way round), that is the problem.
• Enter the key that matches the installed edition. If a PC has Home installed and you have a Pro key, you can upgrade in place: Settings > System > Activation > Change product key, and enter the Pro key. That works without a reinstall.
• If a PC has Pro installed and you only have the Home key, Windows cannot downgrade. Reinstall that PC choosing Home during setup, using the official Windows 11 media from Microsoft's site (the setup asks for the edition, or picks it from the key you type in).
• Enter the key with slmgr /ipk XXXXX-XXXXX-XXXXX-XXXXX-XXXXX, then slmgr /ato, and read the error code if it fails, since each code has a clear meaning.
• If the key says it is already in use on another device, retail keys can be re-activated by phone. Run slui 4, pick your country, and follow the automated steps, or use Contact support in the Get Help app, where you can ask them to release the old activation.

Keep the receipt or the key confirmation email, since support will ask for it. Once each PC has the edition that matches its key, activation normally works on the first try.