refactor(tools/background-task): split tools.ts into focused modules under 200 LOC

- Create modules/ directory with 6 focused modules:
  - background-task.ts: task creation logic
  - background-output.ts: output retrieval logic
  - background-cancel.ts: cancellation logic
  - formatters.ts: message formatting utilities
  - message-processing.ts: message extraction utilities
  - utils.ts: shared utility functions
- Reduce tools.ts from ~798 to ~30 lines (barrel pattern)
- Add new types to types.ts for module interfaces
- Update index.ts for clean re-exports
- Follow modular code architecture (200 LOC limit)

🤖 Generated with assistance of OhMyOpenCode

src/tools/background-task/modules/message-processing.ts

@@ -0,0 +1,75 @@
+export type BackgroundOutputMessage = {
+  info?: { role?: string; time?: string | { created?: number }; agent?: string }
+  parts?: Array<{
+    type?: string
+    text?: string
+    content?: string | Array<{ type: string; text?: string }>
+    name?: string
+  }>
+}
+
+export type BackgroundOutputMessagesResult =
+  | { data?: BackgroundOutputMessage[]; error?: unknown }
+  | BackgroundOutputMessage[]
+
+export type FullSessionMessagePart = {
+  type?: string
+  text?: string
+  thinking?: string
+  content?: string | Array<{ type?: string; text?: string }>
+  output?: string
+}
+
+export type FullSessionMessage = {
+  id?: string
+  info?: { role?: string; time?: string; agent?: string }
+  parts?: FullSessionMessagePart[]
+}
+
+export function getErrorMessage(value: BackgroundOutputMessagesResult): string | null {
+  if (Array.isArray(value)) return null
+  if (value.error === undefined || value.error === null) return null
+  if (typeof value.error === "string" && value.error.length > 0) return value.error
+  return String(value.error)
+}
+
+export function isSessionMessage(value: unknown): value is {
+  info?: { role?: string; time?: string }
+  parts?: Array<{
+    type?: string
+    text?: string
+    content?: string | Array<{ type: string; text?: string }>
+    name?: string
+  }>
+} {
+  return typeof value === "object" && value !== null
+}
+
+export function extractMessages(value: BackgroundOutputMessagesResult): BackgroundOutputMessage[] {
+  if (Array.isArray(value)) {
+    return value.filter(isSessionMessage)
+  }
+  if (Array.isArray(value.data)) {
+    return value.data.filter(isSessionMessage)
+  }
+  return []
+}
+
+export function extractToolResultText(part: FullSessionMessagePart): string[] {
+  if (typeof part.content === "string" && part.content.length > 0) {
+    return [part.content]
+  }
+
+  if (Array.isArray(part.content)) {
+    const blocks = part.content
+      .filter((block) => (block.type === "text" || block.type === "reasoning") && block.text)
+      .map((block) => block.text as string)
+    if (blocks.length > 0) return blocks
+  }
+
+  if (part.output && part.output.length > 0) {
+    return [part.output]
+  }
+
+  return []
+}