If you mean ASP.NET Core 2.1 or ASP.NET Core 2.3, then they are actually .NET Framework despite the name, and are not the same lineage as .NET 10 and .NET 11.
It's still in support, and led to one of the most confusing release announcements in history: https://devblogs.microsoft.com/dotnet/servicing-release-advi...
ASP.NET Core 2.3 does go end of life in April 2027 however: https://devblogs.microsoft.com/dotnet/aspnet-core-2-3-end-of...
It's not that complicated. ASP.net Core 2.2 and earlier was targeted at .NET Standard, so could run in any CLR (CoreCLR or Framework or even Mono, though I don't know how supported mono was). Asp.Net Core is actually just a csharp library like everything else.