PYTHON-5050 Clean up handling of installed dependencies across deployment targets #1350

Job	Run time
Make SDist	39s
Make SDist	39s
Build wheels for manylinux_x86_64	2m 14s
Build wheels for manylinux_x86_64	2m 14s
Build wheels for manylinux_aarch64	10m 45s
Build wheels for manylinux_aarch64	10m 45s
Build wheels for manylinux_ppc64le	2m 25s
Build wheels for manylinux_ppc64le	10m 2s
Build wheels for manylinux_s390x	10m 50s
Build wheels for manylinux_s390x	10m 50s
Build wheels for manylinux_i686	2m 36s
Build wheels for manylinux_i686	2m 36s
Build wheels for win_amd6	5m 0s
Build wheels for win_amd6	5m 0s
Build wheels for win32	4m 41s
Build wheels for win32	4m 41s
Build wheels for macos	4m 32s
Build wheels for macos	4m 32s
Download Wheels	0s
Download Wheels	6s
	1h 35m 7s

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