fix(background-agent): pass model on resume to preserve category config

The resume method was not passing the stored model from the task,
causing Sisyphus-Junior to revert to the default model when resumed.

This fix adds the model to the prompt body in resume(), matching
the existing behavior in launch().

Fixes #826

src/features/background-agent/manager.test.ts

@@ -1036,6 +1036,93 @@ describe("BackgroundManager.resume concurrency key", () => {
   })
 })
 
+describe("BackgroundManager.resume model persistence", () => {
+  let manager: BackgroundManager
+  let promptCalls: Array<{ path: { id: string }; body: Record<string, unknown> }>
+
+  beforeEach(() => {
+    // #given
+    promptCalls = []
+    const client = {
+      session: {
+        prompt: async (args: { path: { id: string }; body: Record<string, unknown> }) => {
+          promptCalls.push(args)
+          return {}
+        },
+      },
+    }
+    manager = new BackgroundManager({ client, directory: tmpdir() } as unknown as PluginInput)
+    stubNotifyParentSession(manager)
+  })
+
+  afterEach(() => {
+    manager.shutdown()
+  })
+
+  test("should pass model when task has a configured model", async () => {
+    // #given - task with model from category config
+    const taskWithModel: BackgroundTask = {
+      id: "task-with-model",
+      sessionID: "session-1",
+      parentSessionID: "parent-session",
+      parentMessageID: "msg-1",
+      description: "task with model override",
+      prompt: "original prompt",
+      agent: "explore",
+      status: "completed",
+      startedAt: new Date(),
+      completedAt: new Date(),
+      model: { providerID: "anthropic", modelID: "claude-sonnet-4-20250514" },
+      concurrencyGroup: "explore",
+    }
+    getTaskMap(manager).set(taskWithModel.id, taskWithModel)
+
+    // #when
+    await manager.resume({
+      sessionId: "session-1",
+      prompt: "continue the work",
+      parentSessionID: "parent-session-2",
+      parentMessageID: "msg-2",
+    })
+
+    // #then - model should be passed in prompt body
+    expect(promptCalls).toHaveLength(1)
+    expect(promptCalls[0].body.model).toEqual({ providerID: "anthropic", modelID: "claude-sonnet-4-20250514" })
+    expect(promptCalls[0].body.agent).toBe("explore")
+  })
+
+  test("should NOT pass model when task has no model (backward compatibility)", async () => {
+    // #given - task without model (default behavior)
+    const taskWithoutModel: BackgroundTask = {
+      id: "task-no-model",
+      sessionID: "session-2",
+      parentSessionID: "parent-session",
+      parentMessageID: "msg-1",
+      description: "task without model",
+      prompt: "original prompt",
+      agent: "explore",
+      status: "completed",
+      startedAt: new Date(),
+      completedAt: new Date(),
+      concurrencyGroup: "explore",
+    }
+    getTaskMap(manager).set(taskWithoutModel.id, taskWithoutModel)
+
+    // #when
+    await manager.resume({
+      sessionId: "session-2",
+      prompt: "continue the work",
+      parentSessionID: "parent-session-2",
+      parentMessageID: "msg-2",
+    })
+
+    // #then - model should NOT be in prompt body
+    expect(promptCalls).toHaveLength(1)
+    expect("model" in promptCalls[0].body).toBe(false)
+    expect(promptCalls[0].body.agent).toBe("explore")
+  })
+})
+
 describe("BackgroundManager process cleanup", () => {
   test("should remove listeners after last shutdown", () => {
     // #given

src/features/background-agent/manager.ts

@@ -397,15 +397,17 @@ export class BackgroundManager {
     log("[background-agent] Resuming task - calling prompt (fire-and-forget) with:", {
       sessionID: existingTask.sessionID,
       agent: existingTask.agent,
+      model: existingTask.model,
       promptLength: input.prompt.length,
     })
 
-    // Note: Don't pass model in body - use agent's configured model instead
     // Use prompt() instead of promptAsync() to properly initialize agent loop
+    // Include model if task has one (preserved from original launch with category config)
     this.client.session.prompt({
       path: { id: existingTask.sessionID },
       body: {
         agent: existingTask.agent,
+        ...(existingTask.model ? { model: existingTask.model } : {}),
         tools: {
           ...getAgentToolRestrictions(existingTask.agent),
           task: false,