Can I vibecode Calendly?

Build me a personal booking page like Calendly. Requirements:

- A public /book page showing my available slots for the next 14 days; visitors
  pick one, enter name + email + note, and get a confirmation page.
- Availability = weekly rules in a config file (e.g. Mon–Fri 10:00–17:00,
  30-min slots, 15-min buffer between meetings, my timezone) minus existing
  bookings, rendered in the visitor's local timezone.
- Google Calendar sync via OAuth (credentials in .env): busy events block slots,
  and confirmed bookings are created in my calendar with the visitor invited and
  a Google Meet link attached. Warn me in the README: this OAuth app setup is
  the fiddly part · budget an hour for the Google Cloud console alone.
- Email confirmations to both sides via SMTP creds in .env.
- Cancel/reschedule links with a signed token in the email.
- SQLite storage, one Node process, no accounts, no framework lock-in.