feat(client): add nginx config for SPA routing and API proxy

- add try_files fallback to serve index.html for all non-asset paths
- proxy /api/ requests to the server container to avoid HTML being
  returned by nginx for API calls when using full route paths

client/Dockerfile

@@ -15,5 +15,6 @@ RUN npm run -w client build
 FROM nginx:alpine AS runtime
 
 COPY --from=builder /app/client/dist /usr/share/nginx/html
+COPY client/nginx.conf /etc/nginx/conf.d/default.conf
 
 EXPOSE 80

client/nginx.conf

@@ -0,0 +1,17 @@
+server {
+    listen 80;
+    root /usr/share/nginx/html;
+    index index.html;
+
+    location /api/ {
+        proxy_pass http://server:3000;
+        proxy_http_version 1.1;
+        proxy_set_header Host $host;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+    }
+
+    location / {
+        try_files $uri $uri/ /index.html;
+    }
+}