Add Playwright test to reproduce booking race condition with calendar cache

refs #22065

Summary

This PR adds a Playwright end-to-end test that ensures we prevent a race condition in Cal.com's booking flow for team events with round-robin host assignment. The test demonstrates how two guests could book the same timeslot within 1-2 seconds when the calendar-cache-serve feature flag is enabled, causing a double-booking issue due to stale calendar cache data.

Key Implementation:

• Creates team event with SchedulingType.ROUND_ROBIN scheduling
• Enables both calendar-cache and calendar-cache-serve feature flags via prisma.teamFeatures.createMany()
• Uses parallel browser contexts to simulate Guest A and Guest B booking simultaneously
• Applies 1.5 second delay between booking attempts to reproduce the race condition window
• Verifies both bookings succeed and queries database to confirm double-booking occurred

Test Results:
The test successfully reproduces the bug locally, consistently showing output like:

Race condition successfully reproduced - both bookings created for same timeslot: {
  sameTimeslot: true,
  host1: 260,
  host2: 261,
  timeslot: '2025-08-01T08:00:00.000Z'
}

Review & Testing Checklist for Human

• Verify race condition reproduction: Run the test locally using TZ=UTC PLAYWRIGHT_HEADLESS=1 yarn e2e apps/web/playwright/booking-race-condition.e2e.ts and confirm it consistently reproduces the double-booking scenario with different hosts assigned to the same timeslot
• Test isolation and cleanup: Confirm the test doesn't interfere with other E2E tests by running a broader test suite and checking that database records are properly isolated/cleaned up
• Review CI failure context: Verify that the E2E (1/4) CI failure is indeed unrelated to this race condition test (investigation shows navigation timeout errors in ab-tests-redirect.e2e.ts and app-store.e2e.ts while this test is not in that shard)
• Validate feature flag logic: Ensure the test correctly enables both required feature flags (calendar-cache and calendar-cache-serve) and that this matches the production scenario where the race condition occurs

Diagram

%%{ init : { "theme" : "default" }}%%
graph TB
    Test["apps/web/playwright/booking-race-condition.e2e.ts"]:::major-edit
    Fixtures["apps/web/playwright/lib/fixtures.ts"]:::context
    TestUtils["apps/web/playwright/lib/testUtils.ts"]:::context
    
    Test --> Fixtures
    Test --> TestUtils
    Test --> PrismaFeatures["prisma.teamFeatures.createMany()"]:::context
    Test --> BookingAPI["/api/book/event"]:::context
    Test --> CalendarCache["packages/features/calendar-cache/"]:::context
    
    Test --> Context1["Browser Context 1 (Guest A)"]:::context
    Test --> Context2["Browser Context 2 (Guest B)"]:::context
    
    Context1 --> BookingFlow1["Booking Flow"]:::context
    Context2 --> BookingFlow2["Booking Flow"]:::context
    
    BookingFlow1 --> Database["Database Verification"]:::context
    BookingFlow2 --> Database
    
    subgraph Legend
        L1["Major Edit"]:::major-edit
        L2["Minor Edit"]:::minor-edit  
        L3["Context/No Edit"]:::context
    end
    
    classDef major-edit fill:#90EE90
    classDef minor-edit fill:#87CEEB
    classDef context fill:#FFFFFF

Notes

• Purpose: This test is designed to prove the bug exists, not fix it. A follow-up PR will tighten the cache TTL to resolve the race condition.
• CI Status: The E2E (1/4) failure in CI appears unrelated to this test based on investigation. E2E shards (2/4), (3/4), and (4/4) all pass, and the failing shard contains navigation timeout errors in different test files.
• Local Testing: The test passes locally with return code 0 and successfully demonstrates the race condition by showing different hosts (e.g., 260 vs 261) assigned to the same timeslot.

Link to Devin run: https://app.devin.ai/sessions/02516b4cc3374102a0d73a11d665ab62
Requested by: zomars (@zomars)