Hello Octavian,
Welcome to Microsoft Community.
Because this series of products is called Surface Pro, but the Pro here does not refer to the professional version.
Please let me answer your questions separately.
1. If I buy the upgrade to Windows 11 Pro via Microsoft Store with the same Microsoft account will it work?
No, they are not related. Pro systems purchased with Alienware computers can only be used with Alienware computers, not with Surface Pro.
2. How does this work? The x86-64 version is attached to one activation key and the arm64 version is attrached to the other?
To be precise, these two purchases do not involve a key, and only a digital license is held in the device.
You have a Pro license in your Alienware computer, so you can use the Pro system in your Alienware computer, but the Surface only has a Home license, so you can't use the Pro Edition in your Surface, and you need to upgrade through the Microsoft Store.
3. Can I install Windows 11 on Surface Pro with only a local account?
Your Surface is already installed with Windows 11 Home Edition, so you can use your local account on this device, but you may receive prompts to sign in to your Microsoft account in some applications, such as Edge, Microsoft Store, because some services are based on Microsoft account. However, it does not affect routine use.
But if you plan to upgrade to the Pro version, you'll need to pay for the upgrade in the Microsoft Store again. So in fact, my advice is that if you don't have any special needs, the home edition is actually enough for you.
That's all the responses to your questions, if you think my response answered your query, please feel free to mark “Yes” or “No” at the top of the response to make it easier for other customers to find the answer faster.
Best Regards,
Mitchell | Microsoft Community Support Specialist