fix(hooks): settle idle prompt continuations

src/hooks/team-session-events/team-idle-wake-hint.ts

@@ -8,6 +8,7 @@ import {
   buildMemberPromptBody,
 } from "../../features/team-mode/member-session-routing"
 import { log } from "../../shared/logger"
+import { settleAfterSessionIdle } from "../shared/session-idle-settle"
 
 type PromptAsyncInput = {
   path: { id: string }
@@ -31,6 +32,7 @@ type TeamIdleWakeHintContext = {
 
 type HookInput = { event: { type: string; properties?: unknown } }
 export type HookImpl = (input: HookInput) => Promise<void>
+type TeamIdleWakeHintOptions = { idleSettleMs?: number }
 
 function getIdleSessionID(properties: unknown): string | undefined {
   const record = properties as { sessionID?: string } | undefined
@@ -41,7 +43,7 @@ function buildWakeHint(unreadCount: number): string {
   return `You have ${unreadCount} new team messages. They will be injected on your next turn.`
 }
 
-export function createTeamIdleWakeHint(ctx: TeamIdleWakeHintContext, config: TeamModeConfig): HookImpl {
+export function createTeamIdleWakeHint(ctx: TeamIdleWakeHintContext, config: TeamModeConfig, options?: TeamIdleWakeHintOptions): HookImpl {
   return async ({ event }: HookInput): Promise<void> => {
     if (event.type !== "session.idle") return
 
@@ -97,6 +99,7 @@ export function createTeamIdleWakeHint(ctx: TeamIdleWakeHintContext, config: Tea
       }
 
       applyMemberSessionRouting(sessionID, memberEntry)
+      await settleAfterSessionIdle(options?.idleSettleMs)
 
       await ctx.client.session.promptAsync({
         path: { id: sessionID },