Make cache clearing robust to directories without read permissions (#… #6157

Job	Run time
cargo fmt	18s
Determine changes	5s
build binary \| linux	1m 58s
cargo test \| ubuntu	4m 6s
cargo clippy \| ubuntu	50s
check windows trampoline	4m 2s
cargo test \| macos	4m 54s
cargo clippy \| windows	3m 7s
build binary \| macos aarch64	1m 28s
build binary \| macos x86_64	1m 57s
build binary \| windows	2m 20s
cargo test \| windows	6m 38s
benchmarks	3m 3s
check system \| homebrew python on macos aarch64	17s
check cache \| macos aarch64	12s
check system \| python on macos aarch64	16s
check system \| python on macos x86_64	24s
check cache \| ubuntu	53s
check system \| python on fedora	36s
check system \| alpine	20s
ecosystem test \| prefecthq/prefect	2m 4s
ecosystem test \| pallets/flask	15s
check system \| amazonlinux	31s
check system \| python on debian	49s
check system \| python on opensuse	39s
check system \| python via pyenv	1m 47s
check system \| pypy on ubuntu	26s
check system \| pyston	3m 50s
check system \| python on rocky linux 8	38s
check system \| python on rocky linux 9	29s
check system \| python on ubuntu	16s
check system \| python3.13 on windows	1m 26s
check system \| python3.12 via chocolatey	1m 28s
check system \| embedded python3.10 on windows	33s
check system \| conda3.8 on linux	43s
check system \| conda3.11 on linux	47s
check system \| python3.10 on windows	41s
check system \| python3.10 on windows x86	37s
check system \| conda3.8 on windows	2m 13s
check system \| conda3.11 on windows	1m 56s
check system \| conda3.8 on macos	54s
check system \| conda3.11 on macos	43s
	1h 1m 29s

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