install: dedup id resolution and make root test robust

[sylvestre]

No description provided.

[cakebaker]

This part of the comment belongs to the behavior function.

[codspeed-hq]

Merging this PR will not alter performance

✅ 331 untouched benchmarks
⏩ 46 skipped benchmarks¹

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_{Comparing sylvestre:test_install_root_combined (9d6476b) with main (4430794)}

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. ↩

[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/date/date-locale-hour (fails in this run but passes in the 'main' branch)
Skipping an intermittent issue tests/date/resolution (passes in this run but fails in the 'main' branch)
Note: The gnu test tests/printf/printf-surprise is now being skipped but was previously passing.
Skip an intermittent issue tests/pr/bounded-memory (was skipped on 'main', now failing)