refactor(hooks): 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/hooks/claude-code-hooks/handlers/session-event-handler.ts

@@ -8,7 +8,7 @@ import { clearToolInputCache, stopToolInputCacheCleanup } from "../tool-input-ca
 import type { PluginConfig } from "../types"
 import { createInternalAgentTextPart, isHookDisabled, log } from "../../../shared"
 import { resolveSessionEventID } from "../../../shared/event-session-id"
-import { promptAfterSessionIdle } from "../../../shared/prompt-async-gate"
+import { dispatchInternalPrompt } from "../../../shared/prompt-async-gate"
 import {
 	clearAllSessionHookState,
 	clearSessionHookState,
@@ -109,7 +109,8 @@ export function createSessionEventHandler(
 				})
 			} else if (stopResult.block && stopResult.injectPrompt) {
 				log("Stop hook returned block with inject_prompt", { sessionID })
-				const promptResult = await promptAfterSessionIdle({
+				const promptResult = await dispatchInternalPrompt({
+					mode: "sync",
 					client: ctx.client,
 					sessionID,
 					source: "claude-code-stop-hook:inject-prompt",