MAUI is actively evolving these days and lots of tutorials appear every day, however, as the main focus is multi-platform, there is almost no specific details about running native apps in classical way, like it was with Xamarin.iOS natively.
So, my main question is actually about how I can launch my MAUI app using a Storyboard, with no xaml pages etc. use (unless there is no other way (at least for the first steps before the Storyboard displayed))?
This is actually a broad question. In context of retiring Xamarin, that seems that it's gonna be quite important question about how to migrate from Xamarin Native (iOS also) projects (which use Storyboards and (possibly) Views) to MAUI. And I can't see any references to that anywhere!
First, what you want is Microsoft.iOS, namely .Net for iOS. Microsoft.iOS is the successor to native Xamarin.iOS and it is the important non-Forms foundation of MAUI.
In Visual Studio 2022 (for Mac), you could find the .NET for iOS template which is called iOS Application. For migration from Xamarin Native projects, you could refer to .NET MAUI Migration docs.
Second, if you want to ask how-to questions, Stack overflow itself is a good place.
But for bug reports or feature requests, you could open an issue on GitHub:
Hope it helps!