Telling people they are talking to an AI
Why disclosure helps you, not just them.
Yes, and you should want to. In several places it is a legal requirement, and everywhere it is a good idea.
Why it helps you
People work it out within a couple of messages anyway. Discovering it after believing they had your personal attention feels like a trick, and that costs more trust than the disclosure ever would.
Told up front, people ask better questions, because they know what they are talking to.
How to do it
Name it clearly: "Sarah's AI" rather than "Sarah". Say it in the greeting. One sentence is enough.
It does not reduce the value
Nobody thinks less of a clone for being one. What they judge is whether it was useful.