Can a .Net 4.8 solution call a Core dll?
Assemblies target runtimes, and some runtimes are "covered" by multiple runtimes.
tl;dr: Entity Framework Core 6+ does not target .NET Framework, .NET Standard, nor .NET Core: it targets .NET 6. You cannot reference .NET 6 assemblies from .NET Framework (1.0-4.8)/Core (1.0-3.1)/Standard (1.0-2.1) assemblies.
Entity Framework Core compatibility:
If you try to install EF Core 7 in a .NET Framework 4.8.1 project:
Could not install package 'Microsoft.EntityFrameworkCore 7.0.5'. You are trying to install this package into a project that targets '.NETFramework,Version=v4.8.1', but the package does not contain any assembly references or content files that are compatible with that framework. For more information, contact the package author.
So the last Entity Framework Core version you can use on .NET Framework is 3, which is ancient and is feature-wise not really comparable to Entity Framework (non-Core) 6.
If we upgraded our EF dll to Core (so that we could apply the latest version of EF to it), would that be likely to break calls to Entity Framework in the rest of our code? Are there syntax changes between the .Net versions of EF and Core versions of EF?
Only about everything. See Port from EF6 to EF Core.
For the inverse, see Can I add a reference to a .NET Framework DLL from a .NET 6 project?.