BUG: Improve DST handling in resample by merging timezone fallback logic and add comprehensive DST test suite

[Chiwendaiyue]

This PR improves the robustness of DST handling in resample operations involving timezone-aware DatetimeIndex, especially for timezones that contain DST gaps such as Africa/Cairo. #62601
What this PR does

1. Fixes NonExistentTimeError triggered by internally generated bin edges
   During resampling, pandas internally constructs bin edges using date_range.
   For certain DST transitions (e.g., Africa/Cairo 2024-04-26), these generated edges may fall into nonexistent local times, producing NonExistentTimeError even when user data does not include such timestamps.

This PR resolves this by:

• Integrating the UTC fallback path directly into _get_time_bins
• Automatically retrying range generation in UTC when encountering a nonexistent time

2. Adds a comprehensive new DST test suite
   A new file pandas/tests/resample/test_dst_handling.py is added.
   It includes:

• Africa/Cairo DST transition tests
• Before-DST and after-DST boundary conditions
• Tests for nonexistent times & shifted times
• Cross-timezone DST behavior (London, New York, Cairo)
• Edge cases: NA values, microseconds, single-point, empty index
• Parametrized frequency tests (2h, 6h, 12h, D)
• Tests matching original issue reports

These tests are API-driven and avoid relying on internal implementation.

No performance tests are added to pytest; those belong to asv.

[jbrockmendel]

Did a human write this?

[Chiwendaiyue]

@jbrockmendel Thanks for the feedback. I'm ashamed and you are right.
But I’ve rewritten the code. Please let me know if further adjustments are needed.