refactor(gateway): gateway↔system1 분리 — gateway=문짝, system1-web=독립

gateway에서 system1 프록시 제거, 대시보드+로그인+공유JS만 담당.
system1-web에 /auth/, /ai-api/ 프록시 이관. tkds-web 제거(gateway 흡수).
notification-bell URL tkfb→tkds, system3 로그인 URL tkds/dashboard로 변경.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

system1-factory/web/nginx.conf

@@ -46,6 +46,46 @@ server {
         proxy_set_header X-Forwarded-Proto $scheme;
     }
 
+    # SSO Auth 프록시 (gateway에서 이관)
+    location /auth/ {
+        proxy_pass http://sso-auth:3000/api/auth/;
+        proxy_set_header Host $host;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+        proxy_set_header X-Forwarded-Proto $scheme;
+    }
+
+    # AI Service 프록시 (gateway에서 이관)
+    location /ai-api/ {
+        resolver 8.8.8.8 valid=300s ipv6=off;
+        set $ai_upstream https://ai.hyungi.net;
+        rewrite ^/ai-api/(.*) /api/ai/$1 break;
+        proxy_pass $ai_upstream;
+        proxy_http_version 1.1;
+        proxy_set_header Host ai.hyungi.net;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+        proxy_set_header X-Forwarded-Proto $scheme;
+        proxy_ssl_server_name on;
+        proxy_read_timeout 180s;
+        proxy_send_timeout 180s;
+    }
+
+    # 레거시 /login, /dashboard → gateway(tkds) 리다이렉트
+    location = /login {
+        return 302 $scheme://tkds.technicalkorea.net/dashboard$is_args$args;
+    }
+    location = /dashboard {
+        return 301 $scheme://tkds.technicalkorea.net/dashboard;
+    }
+
+    # Health check
+    location /health {
+        access_log off;
+        return 200 '{"status":"ok","service":"system1-web"}';
+        add_header Content-Type application/json;
+    }
+
     # Static files (new Tailwind UI)
     location /static/ {
         expires 1h;