…ing busy times

Originally by: keithwillcode

# perf: optimize checkForConflicts by pre-sorting busy times

## Summary

This PR optimizes the `checkForConflicts` algorithm by eliminating redundant sorting operations. Previously, the `busy` times array was sorted on every call to `checkForConflicts` inside the `availableTimeSlots.map()` loop. Now, we pre-sort the `busySlotsFromReservedSlots` array once before the loop and pass a `preSorted: true` flag to skip the sorting step.

**Performance improvement**: Reduces time complexity from O(N × M log M) to O(M log M + N × M) where N = number of available time slots and M = number of busy time periods.

**Changes made**:
- Added optional `preSorted` parameter to `checkForConflicts` function (defaults to `false` for backward compatibility)
- Modified sorting logic to conditionally skip sorting when `preSorted=true`
- Pre-sorted `busySlotsFromReservedSlots` before the `availableTimeSlots.map()` loop
- Updated the `checkForConflicts` call to pass `preSorted: true`

## Review & Testing Checklist for Human

- [ ] **Verify sorting behavior is identical**: Compare the sorting results between old and new code paths with various input data to ensure no behavioral changes
- [ ] **Test performance improvement**: Benchmark with realistic data sizes (e.g., 100+ available slots, 10+ busy periods) to confirm the optimization provides actual benefits
- [ ] **Check edge cases**: Test with empty arrays, single items, and already-sorted data to ensure the optimization doesn't introduce overhead or bugs
- [ ] **Validate backward compatibility**: Ensure existing calls to `checkForConflicts` without the `preSorted` parameter continue to work correctly
- [ ] **Review type compatibility**: Verify that `EventBusyDate` and `BufferedBusyTime` are handled correctly in the sorting logic, especially with different date formats

**Recommended test plan**: Run a local booking flow with various scenarios (multiple busy periods, different event lengths, edge cases) to ensure the optimization works correctly in the full application context.

---

### Diagram

```mermaid
%%{ init : { "theme" : "default" }}%%
graph TD
    A["util.ts<br/>_getAvailableSlots()"]:::major-edit
    B["checkForConflicts.ts<br/>checkForConflicts()"]:::major-edit
    C["busySlotsFromReservedSlots<br/>array creation"]:::context
    D["availableTimeSlots.map()<br/>loop"]:::context
    E["sortedBusyTimes<br/>sorting logic"]:::minor-edit

    A --> C
    C --> |"pre-sorted once"| A
    A --> D
    D --> |"calls with preSorted:true"| B
    B --> E
    E --> |"conditional sorting"| B

    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

- All existing tests pass (31/31 in checkForConflicts.test.ts)
- Type checking passes with no errors
- The optimization maintains full backward compatibility
- This change was requested by @keithwillcode to address performance concerns in the scheduling algorithm
- Session: https://app.devin.ai/sessions/4f20a4a290a2474a8679b6a93053ca2f

<!-- This is an auto-generated comment: release notes by coderabbit.ai -->
## Summary by CodeRabbit

* **New Features**
  * Introduced a preprocessing step to normalize and sort busy time intervals before conflict checking.

* **Bug Fixes**
  * Improved conflict detection accuracy by enforcing sorted input of busy times.

* **Tests**
  * Added tests verifying the sorting requirement and correct preprocessing of busy times for conflict checks.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->