According to this blog entry the language is indeed tied to the framework:

This means that the types required to use these features won’t be available on .NET Framework 4.8. Likewise, default interface member implementations rely on new runtime enhancements, and we will not make those in the .NET Runtime 4.8 either.

For this reason, using C# 8.0 is only supported on platforms that implement .NET Standard 2.1. The need to keep the runtime stable has prevented us from implementing new language features in it for more than a decade. With the side-by-side and open-source nature of the modern runtimes, we feel that we can responsibly evolve them again, and do language design with that in mind. Scott explained in his Update on .NET Core 3.0 and .NET Framework 4.8 that .NET Framework is going to see less innovation in the future, instead focusing on stability and reliability. Given that, we think it is better for it to miss out on some language features than for nobody to get them.

C# 8.0 (and higher) is supported only on .NET Core 3.x and newer versions. Many of the newest features require library and runtime features introduced in .NET Core 3.x: C# language versioning