feat(council-archive): add shared extraction utility and background task type extensions

- Create council-response-extractor.ts with ported extractCouncilResponse()
- Add writeOutputToFile, outputFilePath, _isCompleting to BackgroundTask
- Add writeOutputToFile to LaunchInput
- 8/8 extraction tests passing

src/tools/council-archive/council-response-extractor.ts

@@ -0,0 +1,26 @@
+export const OPENING_TAG = "<COUNCIL_MEMBER_RESPONSE>"
+export const CLOSING_TAG = "</COUNCIL_MEMBER_RESPONSE>"
+
+export interface CouncilResponseExtraction {
+  has_response: boolean
+  response_complete: boolean
+  result: string | null
+}
+
+export function extractCouncilResponse(fullText: string): CouncilResponseExtraction {
+  const lastOpenIdx = fullText.lastIndexOf(OPENING_TAG)
+  if (lastOpenIdx === -1) {
+    return { has_response: false, response_complete: false, result: null }
+  }
+
+  const contentStart = lastOpenIdx + OPENING_TAG.length
+  const closingAfterLastOpen = fullText.indexOf(CLOSING_TAG, contentStart)
+
+  if (closingAfterLastOpen === -1) {
+    const partial = fullText.slice(contentStart).trim()
+    return { has_response: true, response_complete: false, result: partial || null }
+  }
+
+  const content = fullText.slice(contentStart, closingAfterLastOpen).trim()
+  return { has_response: true, response_complete: true, result: content }
+}