Run test suite with `--release-channel=stable`

[tmandry]

This will help us catch failures that occur when the channel is not nightly, like in rust-lang/rust#84950.

We could also run tests for beta, but there are diminishing returns there.

[pietroalbini]

Opened a PR with the fix at rust-lang/rust#86098.

[Mark-Simulacrum]

Closing -- we've done this now.