F# compiler architecture might simply not be suitable. It started as a research project, and its code quality shows that. I don't think Visual Studio ever supported edit-and-continue for F#. Live reload seems to be an upgraded version of that feature.
What's curious, is that the PR that introduces this change is the only PR on the repo that has discussion limited to collaborators only: https://github.com/dotnet/sdk/pull/22217
Editorialized headline, but it is disappointing. The feature is misnamed since it's a VS feature and not a feature for the entire .NET ecosystem (including VS Code).