PYTHON-5050 Clean up handling of installed dependencies across deployment targets #1348

Job	Run time
Build wheels for manylinux_x86_64	2m 21s
Make SDist	37s
Build wheels for manylinux_aarch64	2m 33s
Build wheels for manylinux_ppc64le	2m 35s
Build wheels for manylinux_s390x	2m 34s
Build wheels for manylinux_i686	2m 22s
Build wheels for win_amd6	2m 26s
Build wheels for win32	2m 24s
Build wheels for macos	2m 35s
Download Wheels	1s
	20m 28s

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