Refactor `base_url` extraction logic #106

Job	Run time
macos (macos-15-intel, x86_64)	1m 2s
musllinux (ubuntu-22.04, aarch64)	1m 53s
windows (windows-latest, x64, x64)	2m 11s
macos (macos-latest, aarch64)	40s
musllinux (ubuntu-22.04, x86_64)	1m 45s
windows (windows-11-arm, aarch64, arm64)	2m 3s
musllinux (ubuntu-22.04, x86)	1m 25s
musllinux (ubuntu-22.04, armv7)	1m 25s
sdist	11s
linux (ubuntu-22.04, x86)	1m 57s
linux (ubuntu-22.04, s390x)	2m 13s
windows (windows-latest, x86, x86)	3m 5s
linux (ubuntu-22.04, armv7)	2m 0s
linux (ubuntu-22.04, aarch64)	2m 6s
linux (ubuntu-22.04, ppc64le)	2m 6s
linux (ubuntu-22.04, x86_64)	1m 39s
Release	0s
	27m 41s

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