Telling your customers about it
Disclosure on the call is settled: callers are told at the start, and in a number of places that is a legal requirement rather than a courtesy. What owners actually worry about is different — whether to mention it to the regulars who have rung the same number for eleven years.
What the regulars are actually asking
Not "is this a robot". They are asking whether you are still there — whether the business they chose has quietly become a call centre, and whether the person who knows about their dog is going anywhere. Answer that question and the technology stops being the subject, because it was never really the subject.
The framing that works
"You were getting voicemail at seven in the evening; now you get an answer." That is a benefit to the caller, not an efficiency for you.
Same people doing the work, same number, same everything they care about.
The reassurance is not that it is clever; it is that they are never stuck with it.
Calling it revolutionary invites them to find fault. Calling it "so the phone gets answered" invites nothing.
Where to say it, if anywhere
Most businesses do not need an announcement. A line on your contact page is proportionate, and it gets read by exactly the people who wonder. A mass email is usually a mistake: it tells hundreds of customers who had not noticed that something has changed, and invites opinions on a decision that is yours to make. The exception is a business whose customers are elderly or vulnerable, where a heads-up is a kindness rather than a marketing decision.
What people actually complain about
Not the existence of an assistant. They complain about being stuck in something that will not let them reach a person, about having to repeat themselves, and about being handled by something that did not know the answer and would not admit it. Those are three product problems wearing a technology-shaped costume — get them right and this conversation rarely happens.
Frequently asked
On the call, yes — callers are told at the start, and in several jurisdictions that is a requirement. Announcing it more widely is a separate, optional decision.
Usually not. It tells hundreds of people who had not noticed that something changed, and invites opinions on your decision. A line on your contact page is proportionate.
Answer the question they are really asking — whether you are still there. Same people, same number, and here is how to reach a person.
Being stuck with something that will not let them reach a person, having to repeat themselves, and being given a confident wrong answer. Not the existence of an assistant.