Can I vibecode Appointlet?

Build a robust meeting scheduler application modeled after Appointlet, focusing strongly on flawless timezone support and global team coordination.
The application should use Next.js (App Router), TypeScript, Tailwind CSS, Prisma, and PostgreSQL.

Core Features & Requirements:
1. Public Scheduling Pages:
- Create professional booking pages where invitees can choose meeting types (e.g., "30-Min Discovery Call", "1-Hour Technical Interview").
- Present a clean, easy-to-read calendar interface for selecting dates and times.
- Implement a step-by-step booking flow that collects the invitee's name, email, and any custom questions required for the meeting.

2. Advanced Timezone Management (Crucial):
- Automatically detect the invitee's timezone using browser APIs and display all available time slots in their local time.
- Provide a manual timezone selector in case the invitee is booking for a different location.
- Handle Daylight Saving Time (DST) transitions automatically, ensuring no meetings are double-booked or shifted incorrectly during the changeover.
- Allow the host to define their availability in their own timezone, and ensure the system perfectly translates this across all global timezones.

3. Host Availability & Calendar Sync:
- Build a dashboard where hosts can set recurring weekly hours (e.g., Mon-Fri 9am-5pm EST).
- Support date-specific overrides (e.g., taking Friday the 13th off, or adding extra hours on a weekend).
- Include buffer times before and after meetings to prevent back-to-back fatigue.
- Mock an integration with external calendars (Google/Outlook) where the system simulates reading busy/free blocks to prevent conflicts.

4. Meeting Types & Customization:
- Allow hosts to create multiple meeting types with different durations, locations (Zoom, Google Meet, Physical), and customized descriptions.
- Support multi-host scheduling where the invitee can select a time when ANY of the required team members are free (round-robin or pooled availability).

5. Technical & Design Constraints:
- Use date-fns or Day.js specifically for robust timezone and date manipulations to avoid native JS Date object pitfalls.
- Use server actions and React Server Components for fast initial loads and secure data processing.
- Create a modern, high-contrast, accessible UI using Tailwind CSS and shadcn/ui.
- Include form validation with Zod to ensure email formats and custom questions are correctly filled.
- Ensure the booking interface is fully responsive, looking great on mobile devices.
- Provide a comprehensive README.md explaining how the timezone logic works and how to set up the local development environment using Docker.