refactor(plugin): use unified internal prompt dispatch

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/plugin/event.ts

@@ -43,7 +43,7 @@ import { buildTeamIdleWakeHintClient } from "./build-team-idle-wake-hint-client"
 import { createTeamLeadOrphanHandler } from "../hooks/team-session-events/team-lead-orphan-handler";
 import { createTeamMemberErrorHandler } from "../hooks/team-session-events/team-member-error-handler";
 import { createTeamMemberStatusHandler } from "../hooks/team-session-events/team-member-status-handler";
-import { promptAfterSessionIdle, promptAsyncAfterSessionIdle, releasePromptAsyncReservation } from "../hooks/shared/prompt-async-gate";
+import { dispatchInternalPrompt, releasePromptAsyncReservation } from "../hooks/shared/prompt-async-gate";
 
 import type { CreatedHooks } from "../create-hooks";
 import type { Managers } from "../create-managers";
@@ -510,7 +510,8 @@ export function createEventHandler(args: {
       };
 
       if (typeof pluginContext.client.session.promptAsync === "function") {
-        const promptResult = await promptAsyncAfterSessionIdle({
+        const promptResult = await dispatchInternalPrompt({
+          mode: "async",
           client: pluginContext.client,
           sessionID,
           source: `model-fallback:${source}`,
@@ -527,7 +528,8 @@ export function createEventHandler(args: {
         return;
       }
 
-      const promptResult = await promptAfterSessionIdle({
+      const promptResult = await dispatchInternalPrompt({
+        mode: "sync",
         client: pluginContext.client,
         sessionID,
         source: `model-fallback:${source}:sync`,
@@ -942,7 +944,8 @@ export function createEventHandler(args: {
                 log("[event] compaction before recovery continue failed:", { sessionID, error: err });
               });
 
-            const promptResult = await promptAfterSessionIdle({
+            const promptResult = await dispatchInternalPrompt({
+              mode: "sync",
               client: pluginContext.client,
               sessionID,
               source: "session-recovery:post-compaction-continue",