Best way to install on a NUC

I would argue with that. If you install HA using docker the best way to go on Linux like Ubuntu, because it is harder to configure network from Windows based host. But if you install ubuntu what is the difference with HA OS? None. HA OS also based on Docker with advantage to automate install and update more. You can the same way SSH to your HA OS and run and configure any additional Docker container.

How Ubuntu instalation is different form HA OS if you will not use GUI?

Disagree. In HAOS you do not even get apt-get, plus you probably don’t get to touch the filesystem, so you cannot easily SSH into your HAOS and just “configure any additional Docker container” - at least not without some serious hacking.

Furthermore, even if you successfully configure additional docker container inside the HAOS, your HAOS would start complaining that the OS no long being healthy or supported:
image

So can you do that? Technically yes, if you absolutely have to, and have the time and skillset it takes.
Is it a good idea? Depends, but not likely.
Would I recommend? No.