fix: demo name, trial flow, signup profile fields, docker pgbouncer/frontend

- page.tsx: hero mock shows 'Neha Verma' + 'AI Coach Plan' (was 'Demo Student')
- backend/main.py: demo login maps to Neha Verma UUID (33333333-...)
- backend/main.py: register endpoint stores exam/class/medium/school + trial_end from admin settings
- backend/main.py: register checks allow_new_registrations setting
- backend/main.py: admin student list includes trial_end field
- useActiveUser.ts: rewrite trial logic using real created_at date
- useActiveUser.ts: add computeTrialInfo(), isDemoUser() helpers + expose trialInfo from hook
- useActiveUser.ts: hasAccessTo() now uses effectiveTier from trial logic
- dashboard/layout.tsx: hide demo switcher for real users (only show for known demo accounts)
- dashboard/layout.tsx: trial badge in top header (Day N/15 Trial · Xd left)
- dashboard/layout.tsx: trial day shown in sidebar user card and dropdown
- signup/page.tsx: wire step 2 selects (exam/class/medium/school) to state + send to backend
- signup/page.tsx: success screen shows 'Day 1 of your Free Trial has started!'
- userlist.txt: was empty directory causing pgbouncer mount failure; replaced with proper file
- pgbouncer.ini: added DB credentials in connection string; fixed admin_users
- Dockerfile: added ARG NEXT_PUBLIC_API_URL baked at build time (needed for standalone)
- docker-compose.yml: frontend build arg http://backend:8000; pgbouncer healthcheck; backend waits for pgbouncer

Dockerfile

@@ -19,6 +19,10 @@ COPY . .
 # Set environment variables for build
 ENV NEXT_TELEMETRY_DISABLED=1
 
+# Accept API URL as build arg — defaults to Docker-internal service name
+ARG NEXT_PUBLIC_API_URL=http://backend:8000
+ENV NEXT_PUBLIC_API_URL=${NEXT_PUBLIC_API_URL}
+
 RUN npm run build
 
 # Production image, copy all the files and run next