One agent definition
The adapter owns four things
Transport, the timing model of the channel, the output affordances it can express, and the identity evidence it can report. That is the complete list, and the discipline is in keeping it complete.
The moment a business rule appears in an adapter, the channels begin to diverge - and they diverge quietly, because nobody tests the phone answer against the chat answer.
Rendering, not rewriting
The agent produces one reply. A phone adapter speaks it and discards the attachment. A chat adapter shows the attachment as a card. What an adapter must never do is request a different answer, because that is where factual divergence starts.
The part that does not share cleanly
Knowledge, tools and guardrails share without much trouble. Memory does not, because sharing memory across channels requires deciding that two conversations belong to the same person - and the evidence for that is much weaker on a phone call than in an authenticated session.
The workable rule: below a confidence threshold the agent may verify but not volunteer. It can ask whether this is about Monday's enquiry; it may not open with it.