fix: exclude agent speech from dynamic endpointing pauses

[chenghao-mou]

Problem: An overlap ending before agent playout cleared the agent speech timestamps. Dynamic endpointing then learned the remaining agent audio as an intra-user pause.

Behavior: Preserve the active agent speech interval until playout ends, and pass interruption state as true, false, or unknown. The completed interval prevents agent audio from being learned as a user pause.

Depends on #6939. Original report: #7057. Addresses AGT-3416.

Initial prompt and agent context

Model: GPT-5.6

can you investigate https://linear.app/livekit/issue/AGT-3416/dynamicendpointing-backchannel-during-agent-speech-makes-agent-audio?

okay, then we can bring in the tristate instead

if an user speech outlives an agent speech, that should be considered an input for the next turn, and therefore is not backchannel.

can you create a PR and stack it on 6939?

should we keep the start value by checking _agent_speaking?

yes please add this to the PR

[devin-ai-integration]

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