How do you resolve services from a static or platform context where constructor injection isn't possible?

Expose the app's IServiceProvider. A common approach is a static helper that reads IPlatformApplication.Current.Services, used sparingly at boundaries (e.g., inside a platform callback). Keep such access at the edge and pass resolved services into normal injected code.

public static class ServiceHelper
{
    public static T Get<T>() where T : notnull =>
        IPlatformApplication.Current!.Services.GetRequiredService<T>();
}