feat(background-task): add spawn limit config fields

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

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

assets/oh-my-opencode.schema.json

@@ -3678,6 +3678,16 @@
             "minimum": 0
           }
         },
+        "maxDepth": {
+          "type": "integer",
+          "minimum": 1,
+          "maximum": 9007199254740991
+        },
+        "maxDescendants": {
+          "type": "integer",
+          "minimum": 1,
+          "maximum": 9007199254740991
+        },
         "staleTimeoutMs": {
           "type": "number",
           "minimum": 60000

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

@@ -3,6 +3,54 @@ import { ZodError } from "zod/v4"
 import { BackgroundTaskConfigSchema } from "./background-task"
 
 describe("BackgroundTaskConfigSchema", () => {
+  describe("maxDepth", () => {
+    describe("#given valid maxDepth (3)", () => {
+      test("#when parsed #then returns correct value", () => {
+        const result = BackgroundTaskConfigSchema.parse({ maxDepth: 3 })
+
+        expect(result.maxDepth).toBe(3)
+      })
+    })
+
+    describe("#given maxDepth below minimum (0)", () => {
+      test("#when parsed #then throws ZodError", () => {
+        let thrownError: unknown
+
+        try {
+          BackgroundTaskConfigSchema.parse({ maxDepth: 0 })
+        } catch (error) {
+          thrownError = error
+        }
+
+        expect(thrownError).toBeInstanceOf(ZodError)
+      })
+    })
+  })
+
+  describe("maxDescendants", () => {
+    describe("#given valid maxDescendants (50)", () => {
+      test("#when parsed #then returns correct value", () => {
+        const result = BackgroundTaskConfigSchema.parse({ maxDescendants: 50 })
+
+        expect(result.maxDescendants).toBe(50)
+      })
+    })
+
+    describe("#given maxDescendants below minimum (0)", () => {
+      test("#when parsed #then throws ZodError", () => {
+        let thrownError: unknown
+
+        try {
+          BackgroundTaskConfigSchema.parse({ maxDescendants: 0 })
+        } catch (error) {
+          thrownError = error
+        }
+
+        expect(thrownError).toBeInstanceOf(ZodError)
+      })
+    })
+  })
+
   describe("syncPollTimeoutMs", () => {
     describe("#given valid syncPollTimeoutMs (120000)", () => {
       test("#when parsed #then returns correct value", () => {

src/config/schema/background-task.ts

@@ -4,6 +4,8 @@ export const BackgroundTaskConfigSchema = z.object({
   defaultConcurrency: z.number().min(1).optional(),
   providerConcurrency: z.record(z.string(), z.number().min(0)).optional(),
   modelConcurrency: z.record(z.string(), z.number().min(0)).optional(),
+  maxDepth: z.number().int().min(1).optional(),
+  maxDescendants: z.number().int().min(1).optional(),
   /** Stale timeout in milliseconds - interrupt tasks with no activity for this duration (default: 180000 = 3 minutes, minimum: 60000 = 1 minute) */
   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) */