I know it is possible to add ASP.NET Identity (note NOT Core) to a WebForms project. But what I want to do is add ASP.NET Core Identity to an existing WebForms project.
It is definitely possible to share the database
Option 1: you will need to do some custom implementation since Core Identity (v3) might have a slightly different schema than .NET Framework Identity (v2). Take a look at the following link https://learn.microsoft.com/en-us/aspnet/identity/overview/extensibility/index
You might need to also override the PasswordHasher if they are different implementations. Check the following article out: https://andrewlock.net/exploring-the-asp-net-core-identity-passwordhasher/
Option 2: You can expose login/registering/membership functionality from your Core project and consume from your WebForm as a rest service. There are several rest security schemes and middleware.
See:
Those are a few quick ones. You can probably extrapolate and get some other ideas from looking at the source for Identity lib (https://github.com/aspnet/AspNetCore/tree/master/src/Identity) If you scroll down the readme you'll see different Store providers. For Option 1 you would need to essentially write a Core Store for your Web Forms Identity lib (https://archive.codeplex.com/?p=aspnetwebstack)