run-examples-macos-on-metal job is failing

[alice-i-cecile]

See https://github.com/bevyengine/bevy/actions/runs/25822568493/job/75867370625?pr=24240 for an example of the failure, although it's quite widespread.

See

bevy/.github/workflows/example-run.yml

Line 22 in a399db0

run-examples-macos-metal:

for the job in question.

The logs show that this is calling rustup-init rather than cargo. This appears to be because we've somehow gotten that stuck in our cache. We should be able to clear this as a bandaid, but the bigger problem is that there's a problem in https://github.com/bevyengine/bevy/blob/a399db032194403995eb3b8ed14b3c348e5d36e3/.github/workflows/update-caches.yml

My analysis here is that there are two bugs here:

1. ~/.cargo/bin/ should not be included in our cache, in update-caches.yml, to avoid this sort of problem. We could maybe do better than this, but https://github.com/Swatinem/rust-cache/blob/master/README.md#known-issues suggests to me that this is non-trivial to do correctly.
2. We should be restoring the cache first, then installing the toolchain. This is a non-op if the toolchain is already valid.

1 should fix the current problem, at least when combined with a cache flush. I think 2 is probably worth doing too, but that should be a separate PR that looks at all of our usages of this pattern.

[mockersf]

Cache is being rebuilt from zero every day, so it's not just a "cache caught something wrong" issue

1 could be a problem on the day of a new Rust release if the new version is published after the cache is built, but that's not what we're seeing here. Same for 2