feat(delegate-task): ⚙️ make sync subagent timeout configurable via syncPollTimeoutMs

Allow users to set `background_task.syncPollTimeoutMs` in config to override
the default 10-minute sync subagent timeout. Affects sync task, sync continuation,
and unstable agent task paths. Minimum value: 60000ms (1 minute).

Co-authored-by: Wine Fox <fox@ling.plus>

src/config/schema/background-task.test.ts

@@ -0,0 +1,51 @@
+import { describe, expect, test } from "bun:test"
+import { ZodError } from "zod/v4"
+import { BackgroundTaskConfigSchema } from "./background-task"
+
+describe("BackgroundTaskConfigSchema", () => {
+  describe("syncPollTimeoutMs", () => {
+    describe("#given valid syncPollTimeoutMs (120000)", () => {
+      test("#when parsed #then returns correct value", () => {
+        const result = BackgroundTaskConfigSchema.parse({ syncPollTimeoutMs: 120000 })
+
+        expect(result.syncPollTimeoutMs).toBe(120000)
+      })
+    })
+
+    describe("#given syncPollTimeoutMs below minimum (59999)", () => {
+      test("#when parsed #then throws ZodError", () => {
+        let thrownError: unknown
+
+        try {
+          BackgroundTaskConfigSchema.parse({ syncPollTimeoutMs: 59999 })
+        } catch (error) {
+          thrownError = error
+        }
+
+        expect(thrownError).toBeInstanceOf(ZodError)
+      })
+    })
+
+    describe("#given syncPollTimeoutMs not provided", () => {
+      test("#when parsed #then field is undefined", () => {
+        const result = BackgroundTaskConfigSchema.parse({})
+
+        expect(result.syncPollTimeoutMs).toBeUndefined()
+      })
+    })
+
+    describe('#given syncPollTimeoutMs is non-number ("abc")', () => {
+      test("#when parsed #then throws ZodError", () => {
+        let thrownError: unknown
+
+        try {
+          BackgroundTaskConfigSchema.parse({ syncPollTimeoutMs: "abc" })
+        } catch (error) {
+          thrownError = error
+        }
+
+        expect(thrownError).toBeInstanceOf(ZodError)
+      })
+    })
+  })
+})

src/config/schema/background-task.ts

@@ -8,6 +8,7 @@ export const BackgroundTaskConfigSchema = z.object({
   staleTimeoutMs: z.number().min(60000).optional(),
   /** Timeout for tasks that never received any progress update, falling back to startedAt (default: 600000 = 10 minutes, minimum: 60000 = 1 minute) */
   messageStalenessTimeoutMs: z.number().min(60000).optional(),
+  syncPollTimeoutMs: z.number().min(60000).optional(),
 })
 
 export type BackgroundTaskConfig = z.infer<typeof BackgroundTaskConfigSchema>