Don't know if GP's comment has any backing at all, but the statement that "not all judges agree" is probably literally true (though not necessarily meaningfully true), given that it's a recent case in a district court, issue hasn't been heard in an appeals court yet (presumably), and the fact that all things AI are constantly in flux.
That said I think it's generally a good idea to err on the "safe side" and assume that there's no privilege at all in communications with purported AI lawyers.
The opinion you cited is from an aiphobe judge. Searching ChatGPT is no different than searching Westlaw. If done in anticipation of litigation it’s likely privileged.
note that the client using an enterprise tier does not grant the same privilege.