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Share one path normalizer, home resolver and repository-root walk #1135

Job	Run time
docker composer 2.10.3	8m 47s
composer 2.2.30 / php 8.1 / ubuntu-latest	1m 29s
docker composer 2.2.30	8m 48s
composer 2.9.8 / php 8.4 / ubuntu-latest	1m 16s
composer 2.1.14 / php 8.1 / ubuntu-latest	1m 24s
composer 1.10.28 / php 8.1 / windows-latest	3m 6s
composer 2.2.30 / php 8.3 / ubuntu-latest	1m 26s
composer 2.10.3 / php 8.5 / ubuntu-latest	1m 38s
composer 2.5.8 / php 8.2 / ubuntu-latest	1m 38s
composer 2.9.8 / php 8.4 / windows-latest	3m 12s
composer 1.10.28 / php 8.1 / ubuntu-latest	1m 1s
composer 2.2.30 / php 8.3 / windows-latest	2m 59s
composer 2.8.12 / php 8.4 / ubuntu-latest	1m 24s
composer 2.10.3 / php 8.5 / windows-latest	2m 20s
composer ${{ matrix.composer }} / php ${{ matrix.php }} / ${{ matrix.os }}	0s
composer 2.0.14 / php 8.0 / ubuntu-latest	1m 26s
	41m 54s