feat(eid): 이드 채팅 표면 — /api/eid/chat SSE 스트리밍 + /chat 페이지 (P1)

- compose: eid_chat surface 등록(persona+rules, 자유-prose) + rules_present() 라이브 판정(D-6 fail-closed)
- EidAIClient.call_stream: 닫힌 mode 매핑(daily→mac-mini-default/deep→qwen-macbook), router 경유,
  MLX gate(FOREGROUND)+wall-clock 300s deadline, SSE 라인 relay(model→mode 치환·usage 제거),
  router 400 fail-loud, error_reason allowlist sanitize
- POST /api/eid/chat: JWT, role=system 422 거부, 8000자/40턴/총량 32000 cap,
  503 error_reason(ask 컨벤션), 본문 무로깅
- frontend /chat: 이드 표면 문법(일상/심층, 모델·머신명 비노출), SSE 파서(경계 buf·flush·[DONE]),
  error_reason UX, 8000자 선차단+422 오염 차단, localStorage 이력(logout 시 제거), nav 등록
- Caddyfile: encode 명시 match로 text/event-stream gzip 버퍼링 제외
- tests: 신규 32+ (fixture: router 경유 26B/27B SSE 박제), tests/eid 61 + ask 회귀 9 = 70 passed
- 적대 리뷰 3렌즈 18 finding 반영 13/13. 배포는 D26 게이트(fix/hwp 머지+Soft Lock) 대기

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

app/main.py

@@ -17,6 +17,7 @@ from api.digest import router as digest_router
 from api.document_notes import router as document_notes_router
 from api.document_reads import router as document_reads_router
 from api.documents import router as documents_router
+from api.eid_chat import router as eid_chat_router
 from api.events import router as events_router
 from api.library import router as library_router
 from api.memos import router as memos_router
@@ -174,6 +175,8 @@ app.include_router(documents_router, prefix="/api/documents", tags=["documents"]
 app.include_router(document_reads_router, prefix="/api/documents", tags=["document-reads"])
 app.include_router(document_notes_router, prefix="/api/documents", tags=["document-notes"])
 app.include_router(search_router, prefix="/api/search", tags=["search"])
+# 이드 채팅 표면 (D-1) — POST /api/eid/chat. SSE 스트리밍, EidAIClient.call_stream 봉쇄 경유.
+app.include_router(eid_chat_router, prefix="/api/eid", tags=["eid-chat"])
 
 app.include_router(memos_router, prefix="/api/memos", tags=["memos"])
 app.include_router(events_router, prefix="/api/events", tags=["events"])