1. "Conversation" is purely anthropomorphism. It's software input and output. If the client makes an excel spreadsheet about the cost benefit of ripping off people, it's not work-product.
But the lawyer's draft damages analysis in excel has always been protected.
2. If we're going to buy the "conversation" conceit, lawyers talking to consulting experts have always had a lot more work product protection than testifying experts.
The lawyer talking to Claude feels like talking to a consulting expert, especially since Claude can't have independent knowledge of facts that would allow it to testify.
A spreadsheet I produce for myself probably isn't attorney-client privileged. A spreadsheet or word document I produce for my lawyer can be attorney-client privileged (especially if it's literally only for the lawyer). If a ChatGPT or Claude chat is legally like a spreadsheet, it sounds like it's probably not privileged, but a ChatGPT chat you create "for your lawyer" would be.