the calcom package is not using apache or nginx. Cloudron has an nginx reverse proxy for all apps, but that is outside of the app package itself.
Calcom uses a nodejs based process to serve up api and assets.
You may be able to increase verbosity of that by setting some variables at /app/data/env. Check https://github.com/calcom/cal.com?tab=readme-ov-file#development-tip for the loglevels and env variables.