[Bug] Google API Key 400 Error: Invalid or Missing GOOGLE_GENERATIVE_AI_API_KEY

Bug Description
[긴급 디버깅 요청]
마스터 규칙 11번에 따라 작업을 시작해.

1. 규칙 확인: 오케스트레이션 마스터 규칙 읽기.
2. 상황 파악: 맥락노트 확인 (현재 Google API Key 400 에러 발생 중).
3. 임무: .env.local 파일의 변수명이 GOOGLE_GENERATIVE_AI_API_KEY로 정확한지 확인하고, 서버를 재시작해서 에러를 해결해.
4. 완료 후: [Claude] (날짜) ... 형식으로 맥락노트에 로그 남길 것.

Environment Info

• Platform: win32
• Terminal: vscode
• Version: 2.1.51
• Feedback ID: a3b8e94b-0dda-463a-ba14-66810c50b7dd

Errors

[{"error":"Error: ENOENT: no such file or directory, open 'C:\\ProgramData\\ClaudeCode\\managed-settings.json'\n    at Module.openSync (node:fs:559:18)\n    at Object.readSync (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:9:1291)\n    at Wj (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6487:105)\n    at qH (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6489:224)\n    at J_z (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6473:6011)\n    at nMq (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6473:5788)\n    at file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6473:4481\n    at async cMq (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6473:4857)\n    at async Object.callback (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:12569:391)\n    at async Md8.parseAsync (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6571:4156)","timestamp":"2026-02-24T15:50:43.716Z"},{"error":"AxiosError: Request failed with status code 401\n    at dx (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:90:1138)\n    at IncomingMessage.<anonymous> (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:91:9825)\n    at IncomingMessage.emit (node:events:520:35)\n    at endReadableNT (node:internal/streams/readable:1701:12)\n    at process.processTicksAndRejections (node:internal/process/task_queues:89:21)\n    at kL6.request (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:93:2132)\n    at process.processTicksAndRejections (node:internal/process/task_queues:103:5)\n    at async Cu9 (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:1177:365)\n    at async Y (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:110:19573)\n    at async hu9 (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:1177:508)","timestamp":"2026-02-24T15:50:45.714Z"},{"error":"Error: File does not exist. Note: your current working directory is C:\\Users\\sowon\\OneDrive\\바탕 화면\\ai 도구.\n    at Object.call (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:1981:6271)\n    at async qUY (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:3397:15023)","timestamp":"2026-02-24T15:51:26.554Z"},{"error":"AbortError: The operation was aborted\n    at abortChildProcess (node:child_process:759:27)\n    at AbortSignal.onAbortListener (node:child_process:829:7)\n    at [nodejs.internal.kHybridDispatch] (node:internal/event_target:843:20)\n    at AbortSignal.dispatchEvent (node:internal/event_target:776:26)\n    at runAbort (node:internal/abort_controller:488:10)\n    at abortSignal (node:internal/abort_controller:459:3)\n    at AbortController.abort (node:internal/abort_controller:507:5)\n    at Timeout._onTimeout (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthropic-ai/claude-code/cli.js:6491:2089)\n    at listOnTimeout (node:internal/timers:605:17)\n    at process.processTimers (node:internal/timers:541:7)","timestamp":"2026-02-24T15:51:32.326Z"},{"error":"Error: ENOENT: no such file or directory, unlink 'C:\\Users\\sowon\\AppData\\Local\\Temp\\claude\\C--Users-sowon-OneDrive-------ai---\\tasks\\ad02f36610f7287a0.output'\n    at async unlink (node:internal/fs/promises:1058:10)\n    at async iJ6 (file:///C:/Users/sowon/AppData/Roaming/npm/node_modules/@anthr…

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