Automatically label PRs whose CI results are too stale

[jwnimmer-tri]

To prevent problems like #9468 (and a few other recent instances like it), we would like to prevent merging PRs when their CI results are too stale -- where master has evolved out from underneath them.

We'd like to automatically label PRs whose CI results are too stale -- then we can have Reviewable prevent their merging. (Or maybe the status / label could be just like any other status-check.)

As a start, CI results older than a couple days could be highlighted. You could imagine more imaginative checks, that looks at how much has been merged, or if related packages were touched (even a few minutes ago).

(Discussed in #platform_review slack.)

Over to @EricCousineau-TRI for prioritization.
\CC @jamiesnape

[jamiesnape]

Also relates #10582.

[jamiesnape]

I would probably promote this to medium (and you can assign it to me).

[jwnimmer-tri]

I wonder if https://github.com/apps/stale would be able to implement this? It's been on my wishlist to push forward setting up to automatically close out stale pull requests (those without activity for >6 months). Maybe two birds with one stone.

[jwnimmer-tri]

RobotLocomotion/drake-external-examples#201 is a tryout in drake-external-examples.

[jwnimmer-tri]

We have not had very many stale-merge-race failures recently. We can re-open this if we start to see them again.