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

nginx.conf

@@ -1,26 +1,20 @@
 events {}
 
 http {
-    # Docker's built-in DNS. With the upstreams below held in variables,
-    # nginx re-resolves the service names at request time instead of caching
-    # the address from startup — so a recreated container (new IP) does not
-    # leave nginx proxying to a stale address (502).
+    # Docker's embedded DNS: resolve service names per request (cached 10s).
+    # nginx would otherwise resolve them once at startup and keep proxying to
+    # a recreated container's old IP — a 502 until nginx itself is reloaded.
     resolver 127.0.0.11 valid=10s ipv6=off;
 
-    # "Connection: upgrade" only for real upgrade requests, not every one.
-    map $http_upgrade $connection_upgrade {
-        default upgrade;
-        ''      close;
-    }
-
     server {
         listen 80;
         server_name _;
 
-        # Api Requests
-        location /api/ {
-            set $api_upstream http://backend:5000;
-            proxy_pass $api_upstream;
+        # Api Requests ("/api" without a trailing slash must land here too,
+        # or it falls through to the frontend and loops through its SSR proxy)
+        location /api {
+            set $api_upstream backend:5000;
+            proxy_pass http://$api_upstream;
 
             proxy_http_version 1.1;
             proxy_set_header Host $host;
@@ -28,13 +22,13 @@ http {
             proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
             proxy_set_header X-Forwarded-Proto $scheme;
             proxy_set_header Upgrade $http_upgrade;
-            proxy_set_header Connection $connection_upgrade;
+            proxy_set_header Connection "upgrade";
         }
 
         # Normal requests
         location / {
-            set $frontend_upstream http://frontend:3000;
-            proxy_pass $frontend_upstream;
+            set $frontend_upstream frontend:3000;
+            proxy_pass http://$frontend_upstream;
 
             proxy_http_version 1.1;
             proxy_set_header Host $host;
@@ -42,7 +36,7 @@ http {
             proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
             proxy_set_header X-Forwarded-Proto $scheme;
             proxy_set_header Upgrade $http_upgrade;
-            proxy_set_header Connection $connection_upgrade;
+            proxy_set_header Connection "upgrade";
         }
 
     }