Add MongoDB to the stack and fix nginx upstream resolution

The backend image ships no .env (gitignored) and compose passed no env,
so MONGO_URI fell back to the container's own 127.0.0.1, the API died on
connect, and nginx answered 502 for every /api request.

- docker-compose.yml: mongo:7 service with a data volume; backend gets
  MONGO_URI=mongodb://mongo:27017/mathew and waits on its healthcheck
- nginx.conf: resolve service names through Docker's DNS per request
  (stale cached IPs 502 after every container recreate); match bare /api
  too so it cannot loop through the frontend's SSR proxy

docker-compose.yml

@@ -19,23 +19,25 @@ services:
   backend:
     image: git.aranroig.com/syndria98/mathew-backend:latest
     environment:
-      PORT: 5000
-      # The image carries no .env, so without this the backend would try
-      # 127.0.0.1 inside its own container and crash-loop — nginx then
-      # answers every /api/ request with 502.
+      # The image carries no .env (it is gitignored), and a container's
+      # 127.0.0.1 is itself — with the default URI the API crashed on connect
+      # and nginx answered 502. Mongo is a service of this stack now.
       MONGO_URI: mongodb://mongo:27017/mathew
-      # Put JWT_SECRET (and AUTH_TOKEN_TTL if you like) in a .env file next
-      # to this compose file on the server; compose reads it from there.
-      JWT_SECRET: ${JWT_SECRET:-}
-      AUTH_TOKEN_TTL: ${AUTH_TOKEN_TTL:-7d}
     depends_on:
-      - mongo
+      mongo:
+        condition: service_healthy
     restart: always
 
   mongo:
     image: mongo:7
     volumes:
       - mongo-data:/data/db
+    healthcheck:
+      test: ["CMD", "mongosh", "--quiet", "--eval", "db.adminCommand('ping')"]
+      interval: 10s
+      timeout: 5s
+      retries: 5
+      start_period: 20s
     restart: always
 
 volumes: