refactor(prompt-callers): migrate shared and cli dispatch

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

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

src/shared/session-route.ts

@@ -3,7 +3,7 @@ import {
   promptSyncWithModelSuggestionRetry,
   promptWithModelSuggestionRetry,
 } from "./model-suggestion-retry"
-import { promptAsyncAfterSessionIdle } from "./prompt-async-gate"
+import { dispatchInternalPrompt } from "./prompt-async-gate"
 
 type OpencodeClient = PluginInput["client"]
 
@@ -59,7 +59,8 @@ export function promptAsyncInDirectory(
     return Promise.reject(new Error("session id is required for routed promptAsync"))
   }
 
-  return promptAsyncAfterSessionIdle({
+  return dispatchInternalPrompt({
+    mode: "async",
     client,
     sessionID,
     input: routedArgs,