Windows 11 is not supported on 6th generation Intel processors. Microsoft discusses this in this blog, where they note that a select set of 7th generation Intel, and all 8th generation and above Intel processors are supported, and that 6th generation and below will not be supported. https://blogs.windows.com/windows-insider/2021/08/27/update-on-windows-11-minimum-system-requirements-and-the-pc-health-check-app/
The full Intel CPU compatibility list is available here: https://learn.microsoft.com/en-us/windows-hardware/design/minimum/supported/windows-11-supported-intel-processors, where you can see that the 6770HQ is not on the compatible processors list.
Per the Microsoft blog, their recommendation is to continue running Windows 10 on your NUC, and to upgrade to a newer system that supports Windows 11 before October 2025 when Windows 10 support ends: "For those who are using a PC that won’t upgrade, and who aren’t ready to transition to a new device, Windows 10 is the right choice. We will support Windows 10 through October 14, 2025."
As an unsupported option, you can also use this registry setting to upgrade to Windows 11 while bypassing the CPU support check: https://www.theverge.com/22715331/how-to-install-windows-11-unsupported-cpu-intel-amd-registry-regedit
However, if you choose to do this to upgrade to 11 on your unsupported system instead of staying on 10, note that Microsoft may reserve the right to deny future updates to your system on 11 per https://www.theverge.com/2021/9/21/22686457/windows-11-health-check-compatible-supported-cpu-old-pc-waiver