Add nginx try_files config for clean URL routing

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

Dockerfile

@@ -8,4 +8,5 @@ RUN pnpm build
 
 FROM nginx:alpine
 COPY --from=builder /app/out /usr/share/nginx/html
+COPY nginx.conf /etc/nginx/conf.d/default.conf
 EXPOSE 80

nginx.conf

@@ -0,0 +1,13 @@
+server {
+    listen 80;
+    server_name localhost;
+    root /usr/share/nginx/html;
+    index index.html;
+
+    location / {
+        try_files $uri $uri.html $uri/ =404;
+    }
+
+    error_page 404 /404.html;
+    error_page 500 502 503 504 /50x.html;
+}