Move init_sentry() from module level into the FastAPI lifespan context
manager, immediately after load_settings_from_db() completes. This
ensures that SENTRY_DSN and other Sentry settings configured via the
database admin UI are picked up on every restart.
Also update tests and docs accordingly.
Co-authored-by: christianlouis <361235+christianlouis@users.noreply.github.com>