fix(nudge): route completion notifications through sendUserMessage to fire before_agent_start

[anh-chu]

Problem

sendMessage({ triggerTurn: true }) calls agent.prompt() directly on the underlying SDK agent, bypassing AgentSession.prompt() and therefore the before_agent_start extension event.

Extensions that rely on before_agent_start for per-turn setup (for example, injecting billing or auth context into the provider request) will fail to fire when the orchestrator turn is triggered this way. The result is that the provider rejects the turn with an error and the orchestrator goes silent after a background agent completes. The user has to manually type something to recover.

This happens in both cases:

• Orchestrator idle: sendMessage({ triggerTurn: true }) calls agent.prompt() directly, no before_agent_start.
• Orchestrator streaming: deliverAs: "followUp" queues a continuation via runAgentLoopContinue, which also skips before_agent_start.

Fix

When the orchestrator is idle, send the notification widget and then call pi.sendUserMessage(). This goes through AgentSession.prompt(), which fires before_agent_start correctly.

When the orchestrator is streaming, queue the notification with deliverAs: "nextTurn" so it is included in the next user-initiated turn, which fires before_agent_start naturally. The pi-subagents widget already provides immediate visual feedback in the streaming case.