feat(sisyphus-task): add skillContent support to background agent launching

- Add optional skillContent field to LaunchInput type
- Implement buildSystemContent utility to combine skill and category prompts
- Update BackgroundManager to pass skillContent as system parameter
- Add comprehensive tests for skillContent optionality and buildSystemContent logic

🤖 Generated with assistance of oh-my-opencode

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

@@ -643,3 +643,34 @@ describe("BackgroundManager.resume", () => {
     expect(result.progress?.toolCalls).toBe(42)
   })
 })
+
+describe("LaunchInput.skillContent", () => {
+  test("skillContent should be optional in LaunchInput type", () => {
+    // #given
+    const input: import("./types").LaunchInput = {
+      description: "test",
+      prompt: "test prompt",
+      agent: "explore",
+      parentSessionID: "parent-session",
+      parentMessageID: "parent-msg",
+    }
+
+    // #when / #then - should compile without skillContent
+    expect(input.skillContent).toBeUndefined()
+  })
+
+  test("skillContent can be provided in LaunchInput", () => {
+    // #given
+    const input: import("./types").LaunchInput = {
+      description: "test",
+      prompt: "test prompt",
+      agent: "explore",
+      parentSessionID: "parent-session",
+      parentMessageID: "parent-msg",
+      skillContent: "You are a playwright expert",
+    }
+
+    // #when / #then
+    expect(input.skillContent).toBe("You are a playwright expert")
+  })
+})

src/features/background-agent/manager.ts

@@ -140,6 +140,7 @@ export class BackgroundManager {
       path: { id: sessionID },
       body: {
         agent: input.agent,
+        system: input.skillContent,
         tools: {
           task: false,
           call_omo_agent: false,

src/features/background-agent/types.ts

@@ -41,6 +41,7 @@ export interface LaunchInput {
   parentModel?: { providerID: string; modelID: string }
   model?: { providerID: string; modelID: string }
   skills?: string[]
+  skillContent?: string
 }
 
 export interface ResumeInput {