Hi B W,
I understand why this is confusing, especially since Office 2021 has been working on the same laptop and you have not installed that license elsewhere.
This message does not always mean that Office was manually installed on another physical computer. It can also appear if the activation service starts recognizing the current laptop as a different device, for example after a major Windows or hardware change. The Office 2013 installation on your other PC should be separate from the Office Home & Student 2021 license.
Please first update Office from Word > File > Account > Update Options > Update Now, then restart Word. When the activation message appears again, select Learn more, followed by Contact support to transfer your license to this device. Sign in to the Product Activation Portal with the Microsoft account associated with your Office 2021 purchase. If the license is eligible, the portal may approve the reactivation automatically; select Refresh afterward to complete activation.
Microsoft’s official guidance for this activation scenario is available here: Activate Office after reinstalling or installing on a different device.
If the portal cannot approve the activation and offers a Contact Support option, use it so an agent can review the activation history for the license. Please keep any proof of purchase available, but do not post the full product key publicly. Thank you so much for your understanding.
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