You can not use your .NET Framework 4.8 project with your .NET Core 6 project.
Second opinion https://stackoverflow.com/questions/70923650/how-can-i-use-existing-net-framework-4-8-class-library-in-net-6-project
Regarding compatibility mode
if going this route make sure to test current code and look-ahead and what may come down the road.
In closing, every single one of my Framework 4.8 project were rewritten for .NET Core, didn't want to chance anything along with wanting better performance.