Unknown URLs were returning the app shell with status 200. Return 404 for missing paths, keep the extensionless pages, and send the security headers. Production short links redirect for HeyCatch.
Co-authored-by: Cursor <cursoragent@cursor.com>
## Summary
- Closes#41.
- Stripe live endpoint `we_1TzDNHDV0RPXOyxGCOftavHV` posts to `https://hesychia.ai/api/finance/webhooks/stripe/`. On 2026-10-09 the `chat_web_app` prod vhost returned HTTP 405 fifteen times (`request_time` 0.000, User-Agent Stripe). `pending_webhooks` stayed 1.
- `try_files` falls through to `index.html`, and nginx rejects POST on that static file. The Django handler on `chat_backend` never sees the body.
- `chat_web_app` now proxies `/api/finance/webhooks/` to the same-env `chat_backend` port (`8003` prod, `8013` beta) via `host.docker.internal`. `Host` is the backend public hostname so `ALLOWED_HOSTS` matches. Other static apps are unchanged.
## Test plan
- [ ] `ansible-playbook playbooks/site.yml --syntax-check` (or the web-static portion) renders without error
- [ ] Redeploy web-static (`scripts/deploy.sh` path that runs the web-static role) so `nginx.conf` reloads
- [ ] `curl -i -X POST http://127.0.0.1:8082/api/finance/webhooks/stripe/` from an app host reaches Django (400 invalid signature or 503 missing secret), not 405
- [ ] Stripe Dashboard: resend a failed event to the Hesychia.ai endpoint and confirm 2xx
Reviewed-on: #42
westfarnandCursor