NLS

So, guys this got resolved.
But it is like I write it: IT GOT resolved.
I understand things that happened to me are so weird that some people may think I hide some details. I do not,.

As I said the USB with UNRAID was not booting with my new motherboard in EFI mode, after I made various UEFI setting changes.
So I decided to GO AROUND the issue, go back to CSM (legacy), which with THIS motherboard was a no-go without PCIe gfx card (in other words on-board graphics somehow only allowed EFI booting, no CSM loading - when the cr*p chinese mb I had before, DID allow for that to work, with same CPU).

Anyway, so I went to work next day, tool also UNRAID USB with me to test on a couple other machines.
The content of UNRAID USB was with STOCK 7.0.1 without putting my backup over it.
Also I have arranged to bring an old simple graphics card back home, to enable legacy boot.

In the two machines I tested at work, in BOTH of them USB stick booted in EFI mode! I saw the blue menu!
OK I said, something wrong specifically with my home motherboard (although one of them at work was same brand and similar age with my home one).

So I went home ready to install the graphics card. But first I tried just once more.
STICK BOOTED! IN EFI!
I swear I haven't rouched anything.
Then I thought, maybe I somehow fixed it with the stock and didn't realize.
So I dropped over the stick my own backup of UNRAID USB, but didn't touch the EFI and syslinux folder, plus a few more files I knew didn't differ in version.

THIS WORKED TOO!
So no my UNRAID just... started booting fine in UEFI mode!

So I guess this is a closed issue. Future searches leading to this thread won't be of much help to people.
What I can add as closing comment is that indeed UNRAID SHOULD work in EFI boot mode.
 

...ah I found it.
 

Rebooting the servers seems to have resolved things as I (half) expected.
Yet it would be more useful if we found the cause, because it is a case that can lead to an unstable system.