I just ported a WPF app where the story is similar. Yes, I'd call it "full support". It's not a drop-in replacement, though, except for really simple apps. Check the Breaking Changes List for .NET 6[0], .NET 5, and .NET Core 3.1. Some more niche APIs like `System.Runtime.InteropServices.RegistrationServices` are not supported on .NET 5+ at all. If you have NuGet packages that haven't been updated since 2011 you may need to find modern replacements. There is an Upgrade Assistant tool[1] which can do much of the work. You'll probably have to spend a few annoying hours googling and editing .csproj files by hand.
[0]: https://docs.microsoft.com/en-us/dotnet/core/compatibility/6...
[1]: https://docs.microsoft.com/en-us/dotnet/core/porting/upgrade...