How to implement Comparable so it is consistent with identity-equality

I think the real answer here is: don't implement Comparable then. Implementing this interface implies that your objects have a natural order. Things that are "equal" should be in the same place when you follow up that thought.

If at all, you should use a custom comparator ... but even that doesn't make much sense. If the thing that defines a < b ... is not allowed to give you a == b (when a and b are "equal" according to your < relation), then the whole approach of comparing is broken for your use case.

In other words: just because you can put code into a class that "somehow" results in what you want ... doesn't make it a good idea to do so.

By definition, by assigning each object a Universally unique identifier (UUID) (or a Globally unique identifier, (GUID)) as it's identity property, the UUID is comparable, and consistent with equals. Java already has a UUID class, and once generated, you can just use the string representation for persistence. The dedicated property will also insure that the identity is stable across versions/threads/machines. You could also just use an incrementing ID if you have a method of insuring everything gets a unique ID, but using a standard UUID implementation will protect you from issues from set merges and parallel systems generating data at the same time.

If you use anything else for the comparable, that means that it is comparable in a way separate from its identity/value. So you will need to define what comparable means for this object, and document that. For example, people are comparable by name, DOB, height, or a combination by order of precedence; most naturally by name as a convention (for easier lookup by humans) which is separate from if two people are the same person. You will also have to accept that compareto and equals are disjoint because they are based on different things.