chmod: remove duplicate code handling symlinks

[cakebaker]

This PR is a follow-up to #13842 and removes some duplicate code for handling symlinks.

[cakebaker]

#13872 should be merged first.

[github-actions]

Binary size comparison:

Individual binary size comparison VS main (threshold: >=5% AND >=4 KB).

Total size of compared binaries: 148.93 MB (+320 KB, +0.21%)

Significant per-binary changes:
  install     1.24 MB ->    1.32 MB  (+80 KB, +6.29%)
  mkdir       1.09 MB ->    1.17 MB  (+80 KB, +7.14%)
  mkfifo      1.09 MB ->    1.16 MB  (+76 KB, +6.83%)
  mknod       1.09 MB ->    1.17 MB  (+76 KB, +6.79%)

[oech3]

Sorry for confliction

[codspeed-hq]

Merging this PR will degrade performance by 3.92%

⚠️ Different runtime environments detected

Some benchmarks with significant performance changes were compared across different runtime environments,
which may affect the accuracy of the results.

Open the report in CodSpeed to investigate

❌ 2 regressed benchmarks
✅ 345 untouched benchmarks
⏩ 46 skipped benchmarks¹

Warning

Please fix the performance issues or acknowledge them on CodSpeed.

Performance Changes

	Mode	Benchmark	BASE	HEAD	Efficiency
❌	Simulation	du_max_depth_balanced_tree[(6, 4, 10)]	61.8 ms	64.4 ms	-4.08%
❌	Simulation	du_summarize_balanced_tree[(5, 4, 10)]	16 ms	16.6 ms	-3.77%

Tip

Investigate this regression by commenting @codspeedbot fix this regression on this PR, or directly use the CodSpeed MCP with your agent.

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_{Comparing cakebaker:chmod_remove_duplicate_code (74cb4f8) with main (33df181)}

Footnotes

1. 46 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

[cakebaker]

Your PR was first, no need to apologize :)

[github-actions]

GNU testsuite comparison:

Skip an intermittent issue tests/cut/bounded-memory (fails in this run but passes in the 'main' branch)
Skip an intermittent issue tests/tail/retry (fails in this run but passes in the 'main' branch)