fix(delegate-task): start child prompts reliably

Preserve delegated child prompt/bootstrap metadata for early runtime fallback before OpenCode has persisted the first user turn. Bind prompt gate calls to the SDK session receiver and keep completed background task lookup visible across plugin manager instances.

src/hooks/shared/prompt-async-gate.test.ts

@@ -91,6 +91,36 @@ describe("promptAsyncAfterSessionIdle", () => {
     expect(promptCalls).toBe(1)
   })
 
+  test("#given SDK promptAsync depends on its session receiver #when the gate dispatches #then method binding is preserved", async () => {
+    // given
+    const session = {
+      _client: { accepted: true },
+      async promptAsync(
+        this: { _client: { accepted: boolean } },
+        input: { path: { id: string }, body: { parts: unknown[] } },
+      ) {
+        return { accepted: this._client.accepted, sessionID: input.path.id }
+      },
+    }
+    const client = { session }
+
+    // when
+    const result = await promptAsyncAfterSessionIdle({
+      client,
+      sessionID: "ses_bound_prompt_async",
+      input: { path: { id: "ses_bound_prompt_async" }, body: { parts: [] } },
+      source: "test:bound-prompt-async",
+      settleMs: 0,
+      postDispatchHoldMs: 0,
+    })
+
+    // then
+    expect(result).toEqual({
+      status: "dispatched",
+      response: { accepted: true, sessionID: "ses_bound_prompt_async" },
+    })
+  })
+
   test("#given session.status reports busy #when an internal promptAsync is requested #then no prompt is sent", async () => {
     // given
     let promptCalls = 0
@@ -445,4 +475,34 @@ describe("promptAsyncAfterSessionIdle", () => {
     expect(second.status).toBe("reserved")
     expect(promptCalls).toBe(1)
   })
+
+  test("#given SDK prompt depends on its session receiver #when the gate dispatches #then method binding is preserved", async () => {
+    // given
+    const session = {
+      _client: { accepted: true },
+      async prompt(
+        this: { _client: { accepted: boolean } },
+        input: { path: { id: string }, body: { parts: unknown[] } },
+      ) {
+        return { accepted: this._client.accepted, sessionID: input.path.id }
+      },
+    }
+    const client = { session }
+
+    // when
+    const result = await promptAfterSessionIdle({
+      client,
+      sessionID: "ses_bound_prompt",
+      input: { path: { id: "ses_bound_prompt" }, body: { parts: [] } },
+      source: "test:bound-prompt",
+      settleMs: 0,
+      postDispatchHoldMs: 0,
+    })
+
+    // then
+    expect(result).toEqual({
+      status: "dispatched",
+      response: { accepted: true, sessionID: "ses_bound_prompt" },
+    })
+  })
 })