Backtrack nightly versions when CI fails on nightly but not stable

What problem does this solve or what need does it fill?

NIghtly regularly fails for reasons outside of control. Usually, this is because the latest version broke one of our dependencies.

Typically this is fixed pretty quickly (within a day or two) either in Rust or upstream. But until then, we can't merge PRs.

When the crate build on stable (but not nightly):

For an example of the most recent breakage, see #5330, caused by the problem fixed in NotIntMan/inplace_it#11

See this Zulip thread for a discussion with the Rustlang team about possible solutions on both ends.

That could be quite hard to do with GitHub actions... and backtracking could be very costly (in time)

I would prefer:

run nightly on a cron
report status to an external "database" (could be a git repo... preferably another repo to avoid too many commits to this one)
in CI, use the last reported nightly

That wouldn't add a lot of complexity to existing CI, but we would need a place to report the status

doesn't happen often enough to be a pain, and it's nice to know of breakage to raise issues on rust-lang