fix(interruption): keep the overlap armed when agent speech restarts mid-interrupt

.changeset/adaptive-interruption-overlap-state.md

@@ -0,0 +1,22 @@
+---
+'@livekit/agents': patch
+---
+
+fix(interruption): keep adaptive interruption armed when agent speech restarts mid-overlap
+
+`overlapSpeechStarted` is the gate that lets a user's overlapping audio reach the interruption
+model, and only a VAD start-of-speech raises it. Two events cleared it while the user was still
+talking, and because VAD never re-announces speech that is already under way, nothing could re-arm
+it for the rest of the agent turn: every remaining frame was dropped, no inference request was
+made, and the agent talked straight through the interruption.
+
+- A transport failover rebuilt `InterruptionStreamBase` from scratch and replayed only
+  `agent-speech-started`, which marks the agent as speaking but leaves the overlap disarmed. The
+  in-progress overlap is now handed to the replacement stream.
+- A second speech segment in the same turn (a queued `SpeechHandle`, or the reply after a tool
+  call) raises `agent-speech-started` again with no `agent-speech-ended` in between, and was
+  treated as a new turn. An open overlap is now preserved across it; a genuine new turn still
+  resets the overlap, audio buffer, cache and counters.
+
+Also stops a rejected forwarding task from surfacing as an unhandled rejection during the failover
+backoff.