Alexander Khrgian, it's clear to me now from the screenshot and error code 0xC004F014 on the old machine. It confirms exactly what has happened: the old machine is not "freeing up" the license; it is simply stripped of its credentials.
In the Windows licensing architecture, a license being "not activated" on one machine does not automatically make it "transferable" to another. Transferability is defined by the License Channel (OEM/GGK vs. Retail), not by its current activation status. Your GGK license is legally and cryptographically bound to the Unique Hardware ID (UHID) of the old motherboard. By running slmgr /upk on the old machine, you didn't "detach" the license rights to make them portable; you simply deleted the local key from the registry, leaving the old OS in an unlicensed state (hence error 0xC004F014, which translates to "Product key not available").
The error on your new computer (0xC004E016) indicates that the Software Licensing Service sees the key format but rejects it for the installed OS edition or channel. This is the system's way of enforcing the OEM restriction. Because the key is a Windows 8.1 Pro GGK (OEM) key, the activation servers recognize it is being input into a Windows 10 environment on a different hardware hash than where it originated. The server rejects the handshake immediately because the "Down-Level" rights (using an 8.1 key for 10) for OEM keys are only valid on the original hardware.
You saod the old computer now also says "Invalid Product Key." This is likely because the digital entitlement was deleted from your MS Account cloud dashboard. However, since the hardware hasn't changed on the old PC, you can likely restore its activation by running slmgr /ipk <YOUR-25-DIGIT-KEY> on the old machine. It should re-associate with the hardware hash.