Edit 18.08.2022 (added)
"The Register" has some more details:
I quote, "Limit your expectations to server-side stuff. This is a mainly a way to deploy console-based C# and ASP.NET apps into Ubuntu servers and Ubuntu containers.".
Summary
This does not look as if it will have a direct impact on the desktop Linux.
Red Hat has had this ability since Fedora 36 (see The Register article cited above)
As far as I know ".NET" is an 'application developement framework' similar to GTK (Gnome software) and Qt (KDE software). This affects software developers.
Some may also find it to be of interest as it further describes the extent to which Canonical and Microsoft are collaborating with each other.
And the answer I can find is: I don't know. It's a toss-up. Supposedly not every part of .NET has ever been ported to any operating system besides Windows, but I'm not familiar with what components of .NET Paint.NET uses.
I'm hoping somebody else has more familiarity with the subject than I do. (The only reason I posted was to decode what @Frieder_Saugschmerle said.)
So don't get excited and think that the inclusion of .NET in Ubuntu means that graphical .NET apps, such as Windows Store apps, can now be built and run natively on Linux. Limit your expectations to server-side stuff.
Just from reading that quote I'd expect the answer to be "No", but again sorry I don't know.
I have no special knowledge here, my only interest is related to my Ubuntu News [hat]