My guess is that a lot of problems will be resolved once you move away from the static DataAccess class. It seems that your legacy app spun its own Factory-like scheme that can be handled cleanly using native .NET & EntityFrameworkCore.

DbContext instances (or DbContextFactory instances) can be set up to be available from the IServiceProvider, or injected directly into controllers or other service classes. DbContexts or DbContextFactories will get their connection strings within the static Main method, where you build your IConfiguration to go into the IServiceProvider and can pull connections strings at the same time.

Is each DataAccess the same DbContext or are there different tables, etc., involved? If they are the same, create a projects for your DAL from which each of your other projects can depend.