It looks like the answer to your question is no for .NET 5/6, if I'm correctly understanding Microsoft's documentation. It looks like the latest version you can use with .NET Framework is .NET Standard 2.0.
.NET Standard is a formal specification of .NET APIs that are
available on multiple .NET implementations. The motivation behind .NET
Standard was to establish greater uniformity in the .NET ecosystem.
.NET 5 and later versions adopt a different approach to establishing
uniformity that eliminates the need for .NET Standard in most
scenarios. However, if you want to share code between .NET Framework
and any other .NET implementation, such as .NET Core, your library
should target .NET Standard 2.0. No new versions of .NET Standard will
be released, but .NET 5, .NET 6, and all future versions will continue
to support .NET Standard 2.1 and earlier.
If you're building reusable libraries that you plan to ship on NuGet,
consider the trade-off between reach and available feature set. .NET
Standard 2.0 is the latest version that's supported by .NET Framework,
so it gives good reach with a fairly large feature set. We don't
recommend targeting .NET Standard 1.x, as you'd limit the available
feature set for a minimal increase in reach. If you don't need to
support .NET Framework, you could go with .NET Standard 2.1 or .NET
5/6. We recommend you skip .NET Standard 2.1 and go straight to .NET
6. Most widely used libraries will multi-target for both .NET Standard 2.0 and .NET 5+. Supporting .NET Standard 2.0 gives you the most reach, while supporting .NET 5+ ensures you can leverage the latest
platform features for customers that are already on .NET 5+.