From https://www.noesisengine.com/forums/viewtopic.php?t=2821

So, I figured out the memory leak issue. It is indeed a bug in our code, but a very odd one, so I suggest you to take a look into it on your side as well or at least document it.

First, while picking apart literally everything inside our resources, I noticed the memory leak only happens if there are TextBlock or TextBox objects in the resources (e.g. in some control templates). The more instances of TextBlock/Box there are the larger the leak.
Then, while trying to remove as much code as possible between load and Shutdown, I noticed we have following lines that are absent from your examples:

Noesis::GUI::SetTextureProvider(0);
Noesis::GUI::SetXamlProvider(0);
Noesis::GUI::SetFontProvider(0);

This code wasn't written by me, but I never paid attention, because it looked like a reasonable thing to do. Turns out it isn't :)
Setting Font provider to null like this causes a memory leak on Shutdown if I have TextBlocks inside resources!
It is also reproducible in your examples, simply by adding GUI::SetFontProvider(0); before Shutdown